Which different styles exist (Kufi, Nashk etc.) and which are the differences between them?
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Are the Arabic types divided in Text- and Display fonts like the Latin typefaces?

Several Arabic calligraphic styles developed from different Arabian cities, different Arabic eras, different writing techniques and different writing tools. The most known Arabic calligraphic styles are: 1-Kufi, 2-Thuluth, 3-Diwani, 4-Naskh, 5-Persian (known as Nastaliq), 6-Ruqaa and 7-Maghrébi.

The name of the Kufi originated from the city Kufa in Iraq and it said to be the oldest Arabic calligraphic style. The kufi style is the only geometric style that can be drawn by a pencil and a ruler; all other styles are modulated and written by the brush or the bamboo stick with ink. There are three kinds of Kufi. The Archaic Kufi, The Ornamented Geometric Kufi and The Square Kufi.

The Naskh and Diwani originated during the Ottoman Empire. The Naskh is named after the ‘naskh’ (copying and writing) action when the scribes used to copy the Arabic books and other documents by hand. The Diwan name is originated from the political documents that are named in Arabic ‘Diwan’. The Diwani style was used for the important imperial and governmental documents since it was more calligraphic and cursive, while the Naskh was used for the everyday writings and documents since it is more standard and easier to read in long text.

The Thuluth name originated from the names of several bamboo sticks that were used as tools for writing.

The Ruqaa name originated from the leather paper ‘Ruqaa’ that it was written on.
The Ruqaa is the everyday Arabic handwritten style. It is the most simplified script of the others. Most Arab people write in the simplified Ruqaa style nowadays.

The Persian style originated its name from the Persian language. The Nastalid is close to the Ruqaa style is feel and structure. It is mostly used in Iran nowadays.

Today, most of the text typefaces available are based on the Naskh or the Thuluth Style. The other styles like the Kufi, Diwani and Maghrébi are used as display typefaces.

Has religion an influence on Arabic type?

The Islamic religion was behind the unification of the Arabic script and the creation of its grammar. The Arabic script before Islam was so primitive and during the early years of the Islam, the script was developed to the point that we know it today. Since the Arabic language is considered the language of God in Islam, the Arabic language had to be standardized and make it possible for the believers to learn it in order to pray and follow the guides of God. The Islamic conquers and spread through out the Middle East and North Africa until Spain, made the Arabic script and language spread in a fast manner and utilized by a large number of people on earth. Through out the reign of the Islamic and afterwards the Ottoman empires, several Arabic calligraphic scripts were created from different cultural and geographic areas or due to different writing techniques.

The Arabic script had to be beautified since it is the language of God. Ornamental and floral elements were always added to the letters and words that addressed religious content.

Though the Arabic script and language is strongly linked to the Islamic religion, the Arabic script should be viewed independently and not always linked to Islam. The Arabic script is a writing system like any other writing systems. People should not be afraid it and always link it to orthodox Islamic movements and acts. The Arabic script is an art as well as a writing system. Nowadays, Arabic typefaces are being created frequently, and type designers are enjoying the freedom to play around with it and create contemporary outlines. Arab and non-Arab designers should not be afraid of playing around with the Arabic type and create new forms.

Were there any new developments (technical and design) in the last years?

Taken from the article on my blog.
History of Arabic Type Evolution from the 1930’s till present.
https://29letters.wordpress.com/2007/05/28/arabic-type-history/
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4. WHAT IS THE FUTURE OF ARABIC TYPEFACES?
The following question was asked in the TypoGraphic Beirut 2005 conference that took place in April in the Lebanese American University.
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There are three main directions in the Arabic type design word nowadays. The first direction is represented by Arabic type designers and typographers who are working on simplifying the Arabic script and making it detached. The second direction is backed up by conservative traditional Arabic type designers who state that the Arabic does not need to be simplified any more since the technology is now well developed to accommodate all the needs/problems of an Arabic calligraphic typeface. The third direction is represented by several contemporary Arabic type designers who’s work deals with making modern Arabic typefaces which are legible and friendly to the everyday applications or to the need of their clients. An example of the first group is Saad Abulhab, the second group is Thomas Milo and the third group are several independent Arabic type designers (like Nadine Chahine, Titus Nemeth, Tim Holloway, Abbar Yassar, Ihsan Al-Hammouri, Mohamed Hacen, several others and surely myself) that are creating new modern Arabic typefaces. Names and links of know independent Arabic type designers and Arabic type foundries will be listed in the section that follows.
Whatever the direction or the intentions behind each new Arabic typeface, there is a big demand for new Arabic fonts. New Arabic fonts are need for: 1. everyday Arabic graphic design and typography projects, 2. corporate Arabic fonts for Arabic established companies or newspapers, and 3. Arabic companion fonts for existing Latin fonts.
Professional graphic designers and students are always asking for new Arabic
fonts. Before the launch of Adobe InDesign ME versions and the development of the OpenType Arabic fonts, most of the Arabic typographer used Quark AXt and were limited to AXt Arabic fonts. Until now the AXt fonts are the most used even-though the users of Quark AXt is diminishing. The reason for that is there are not so may new OpenType Arabic fonts for them to use instead of the AXt fonts. Over the last few years, the awareness about Arabic type and the need for new fonts was translated in the rise of Arabic Type Foundries and young Contemporary independent Arabic Type Designers. From the past three years there was Nadine Chahine, Titus Nemeth and myself Pascal Zoghbi who have graduated with Masters in Type Design and are specialized in Arabic type. All three of us now are working and developing new Arabic fonts that are starting to appear in the Market.
The Khatt Foundation ‘Typographic Matchmaking’ project is an example about the need for Arabic type companions for existing Latin typefaces (you can read more about the Typographic Matchmaking project and the Khatt foundation in the ‘Typographic Matchmaking: Arabic type with a Dutch flavor.’ post on my blog or on the Khatt Foundation website). This is due to the fact that many publications in the Arabic nations are bi-lingual or tri-lingual (Arabic, English and french). Another reasons is that most of the international companies how are opening new branches in any of the Arab nations need an Arabic corporate font that will work with their own Latin corporate font.
Other important typographic events that contributed to the growing awareness of Arabic type and calligraphy are: Typo.Graphic.Beirut conference, The Kitabat conference, The Linotype’s First Arabic Type Competition and Khatt Kufi & Kaffiya symposium.
Corporate Arabic fonts are also in need for new Arabic companies how are building there new identity. Some examples will be Banks, Communication companies, Organizations and others. Furthermore, all of the Arabic newspapers at the present time are asking for corporate fonts. Old Arabic newspapers are renewing their layouts and asking for new modern Arabic fonts, and new rising Arabic newspapers are creating their young fresh identity with new contemporary corporate Arabic fonts.

At the present moment the Arabic type industry is having a big boom and it is going to stay like this for a while (at least several years). The awareness about Arabic type is growing in the Arab nations and the number of professional Arabic type designers is increasing.
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Speaking only technically, with the presence of Arabic OpenType technology and the production of Adobe CS ME applications, the creation and use of Arabic fonts became much more easier and friendly.
U can also check another article I wrote about creating and developing Arabic fonts.

Generating Arabic fonts
https://29letters.wordpress.com/2007/05/15/generating-arabic-fonts/