I have heard that when you start taking T, your breasts do get a little smaller over time. Does this means the nipples themselves get smaller as well? 

And I was also wondering, since binding actually changes the breast tissue, and they are just pretty much fat from there (I thiiink ), would it be possible to turn that fat into muscle, say if you were currently an A cup? Since I've noticed most female body builders have really really small breasts

Alas, no, the nipples stay the same size unless you have them surgically reduced.  As for overall breast size, it varies a lot from person to person.  Some people have a lot of solid breast tissue in there, and don't change much in size.  Others change dramatically.  I know one guy who started as a large B pre-T and ended up small enough that he became a candidate for peri-areolar surgery.  Most seem to go down about a cup size.

No unfortunately nipple size stays the same andbreast sizes varies person to person. Some people say that from binding and t theirs pretty much go flat but I've been binding for almost 2 years and been on t for 8 months and I still have a lot of solid breast tissue the little bit of fat that was there is gone and that made them a little smaller but not a whole lot.

And I don't know if that fat can be turned to muscle... I know you can build your pecs up but I don't know if that is the same thing...

From what I've heard building your pecs up just pushes the breasts out from beneath.  Which can make them look bigger.  Talk about a step backwards. 

It's one of the reasons a lot of guys end up getting top surgery even if they didn't originally intend too.

The fatty tissue in your chest will redistribute in a more masculine way while on T. However, if you are a chubby guy with a large chest you'll end up with a whole bunch of excess skin. Nipples won't shrink and neither will the skin around it.

I did a lot of working out last summer, especially the pec area, and the moobs got smaller.  But mine are mostly fat, so your mileage may vary. 

it depends on if the size is because of fat vs. Nature. If fat,you can lose some size over time regardless. If it's Nature, working out will push them out. T will help redistribute fat so it doesn't go to your chest. However, it'll go to your stomach if you're not careful... Watch that. XD