My AS son had terrible problems with food when he was this age. The psychologist advised us to serve mainly things that we knew he would eat but with a very small amount of a disliked food on the plate (even if it was only one pea.) THe child has to at least make an attempt to eat the food, again even if it is only one pea. AS you go on, you can increase the amount of the hated thing very gradually. Eventually, the old stuff should be able to be supplemented/replaced with the new stuff and an almost normal diet can be achieved. We had to avoid (and still have to) vinegary foods/strong smelling foods/cheese unless its pizza! When confronted with a meal that he just wouldn't/couldn't eat, we had to offer a very simple alternative like cereal or a basic sandwich. And ALWAYS reward the effort made to tolerate the stuff that he doesn't like.
With regard to the food touching each other, that used to cause havoc in here, screaming tantrums, vomiting the lot. What we had to do was VERY gradually move things closer together on the plate, at a rate which was almost imperceptible, but we also had to tell DS what we were doing. The same goes for things like cutting sandwiches and things. DS2 would only eat square cut halves, not triangles, not quarters, nothing but square cut halves, or there would be scenes of carnage. We had to very, very slowly change the angle or off-centredness of the cut (not at the same time.) Again, we had to talk to him about this and gradually increase his level of tolerance.
It can take years, though. We were still doing the not touching stuff and the sandwich stuff when DS2 was 15, (he's 17, now.) He mostly eats quite normally now as long as we avoid things that we know he really can't eat (most green things/vinegary or strongly smelling things/raw veg/cheese/potatoes) because they set off his sensory processing problems and sensitivities. Sometimes, you just have to resign yourself to things and deal with what you can.
I don't expect your DS will be as extreme as mine, though!