This is not my field per se, and you're asking rather broad questions, so I'll do my best. Anyone who knows better is free to correct any errors. Also, some of these photos may be large, if there's a way to change the size to make them more forum friendly, let me know. Not sure if that'll help this time (sorry Salpy!), but for next.
As I've said before, after the arrival of the Portuguese and the ravages they inflicted on the native Church, there wasn't much left in terms of books, records, etc. of the first fifteen hundred years of Christianity there. Some things have survived here and there, but not enough to begin to answer a lot of the questions we have.
But with that disclaimer, I'd venture to say that the use of icons in India was certainly limited, much more so than among Copts, Ethiopians, and the EO. I don't think it was because they were considered idolatrous, though. One might suppose that, because the Hindus are certainly idolaters, Christians went in the opposite direction. While such a hypothesis seems plausible, it doesn't account for how quickly everyone adopted the use of images after the Portuguese arrived: after all, if the tradition was always in opposition to another practice, then certainly the profusion of images in Portuguese RC tradition would've inspired a similar distaste for images among the non-Catholics. And yet, you have to wait another couple of centuries before you get a group of native Christians who reject the use of images in worship as precisely a type of idolatry (the so-called "Mar Thoma Church", a Protestant denomination which broke away from the Orthodox Church due to Anglican missionary influence).
The non-use of images in worship in the pre-Portuguese era of Indian Church history probably has more to do with its strong ties with the tradition of the Persian Church (and this relates to your second question). The Syriac Churches don't have a highly developed tradition of icons. The Eastern Syriac (i.e., Persian) Church certainly didn't have them, and the Western Syriac (Antiochene) Church likely had some tradition of icons (e.g., the tradition of Syriac iconography in illuminated manuscripts), but hardly "mandatory" and greatly influenced by other iconographic traditions. This can appear to EO observers as a rejection of icons, but in fact is simply the continuation of an older, pre-iconoclast tradition, while the EO tradition of iconography which we have to this day certainly developed by leaps and bounds after the iconoclast period.
In the Syriac traditions, the veneration of the Cross is prominent in ritual, private devotion, and church art. Similarly, the book of the Gospels traditionally occupies the place in our parishes that an analogion with the icon of the feast or parish patron has in EO churches, and is similarly venerated. Because the walls of the church are consecrated with Chrism, it's not unheard of for the walls to be venerated or otherwise treated with honour by the pious. Because of India's links with Persia, I think that the "original" tradition in India was the non-use of icons in worship. The Cross and the Gospel featured more prominently, especially the Cross. There are very ancient stone crosses preserved in some of the churches.
An example of an ancient, traditional stone cross:
Two such crosses, one at the Northern side altar and one at the Southern:
A close-up of the Northern side altar cross:
All churches today, whether or not they are also adorned with icons, have an adorned Cross on the altar, as you may notice in the photos.
Perfectly acceptable examples of a sanctuary without icons (Syriac, but I don't know where these are):
East Syriac (Assyrian Church of the East, India first and then some parish named Mar Sargis that I can't seem to find any info about):
Or with minimal icons (St Mark Syrian Orthodox Monastery, Jerusalem):
Also, the courtyard of a number of larger Indian churches, outside the narthex, will typically have a large stone Cross. Most churches also have a roadside shrine in which the Cross is kept, whether or not icons are also enshrined therein.
A typical example--the current St Mary Syro-Malabar Catholic Church, founded in AD 999, centuries before the Latins came in:
A typical roadside shrine--St Thomas Orthodox Church, South Pampady:
But that doesn't mean that there were no images in the churches. To a certain extent, we can't ever know definitively. Many of the older churches have fallen into disrepair or were destroyed and replaced with newer buildings. But in a number of the older churches we do have, there are wall paintings and even carvings of scenes from the Bible or from the lives of saints. Certainly, some of these demonstrate Portuguese influence, but there are older murals which show native art adapted to Christian needs. For example, take a look at some of the images at http://nasrani.net/2007/05/01/the-mural-tradition-of-nasrani-churches-in-kerala/
Or look carefully at the upper side walls of the sanctuary of this Indian church:
Or on the altar of the chapel of St Nicodemus (Church of the Resurrection, Jerusalem):
Icons aren't rejected in our tradition, but they aren't for us what they are for the EO. Theologically, our views on icons are similar, but our historical relationship with them has been quite different, and has shaped the piety of the EO in ways that haven't happened for us. But that is not to say that the people do not venerate them. They honour them in churches and shrines and keep them in their homes, but how this is done is left to the piety of the individual believer rather than the legislation of the Church. The Church doesn't mandate forms of veneration or even that images be present/absent from churches. Ecclesiastical arts in the Syriac tradition are not so much concerned with icons as they are with music, architecture, etc., but it's not as if images are unheard of.
I don't know if this helps any. At least I hope you enjoyed the eye candy.