You mean texturing in PS using the 3D painting method? I don't know how well that works or whether you have to UV the model first, but I suspect so.
1) You'll probably have to UV it, not necessarily planar
2) No, it doesn't work perfectly, you'll have to tweak it and sew some UVs together
3) Obj should work fine I think if you're doing the 3D method
For texturing in Photoshop the normal thing to do is to create a flat UV map in Maya and export that, I don't know too much about the 3d functions as I haven't used them but like mastone said you'd probably be a lot better off using another application for that. Depending on what kind of model you have and how clean your geometry is this can be a really easy process or it can take as long as the modeling process itself. For something like an interior scene you get away easily with automatic mapping for most things, on a character UV's are more complicated and you'd need to use planar, cylindrical etc.
I just wanted to mention here that there are a lot of plug-ins available for UV layout that will do the job for you, it's a bit of a cheat and I just watched a tutorial with Jay who's a really good modeler where he mentioned the fact that there are certain advantages to taking this hard route and laying out flat UV's. So as a modeler this is something you must know, but also for a quick result and to get yourself started with texturing in Photoshop you can try a plug in to get a better idea, the one we have here is unwrella it's not too expensive and you can download a trial version here https://www.unwrella.com/download/