Welcom to the forums! This is a great forum for New England gun owners and shooters. Make sure you check out all of the different threads going on. There's a lot of good info out there.
I live in CT and am an instructer. To answer your questions quickly:
#1, no, Federal Law says you can't buy a handgun in CT. However, it can be shipped to your FFL/Dealer in MA for xfer to you there. You CAN buy a long gun, however, since you have a MASS license and a CT license. Handguns have to be xfered by an FFL to the new owner in the state where they reside.
#2, A private CT citizen can not sell you a handgun because you are not a citizen of CT.
Regardless of what permits you have you're restricted to buying handguns from the state you live in unless you have the seller send the handgun to an FFL in your town where they will do the xfer for the seller to you in your home state.
I've got a MA non-res permit and I can't even buy ammo in your state......nothing...not even .22 or shotgun shells even with a LTC-a AND a hunting license. However, the CT permit will allow you to carry your handgun with you. We don't have any 'concealed carry' laws, either. There isn't one single word about carrying concealed in our regs. HOWEVER, no one carrys open here anymore unless you want a lot of unnecessary attention. Conceal carry will work just fine, however. You can also buy all the ammo you can load into your car. We have no ammo restrictions nor mag restrictions. However, MA does as I'm sure you know and your purchases should reflect those restrictions (10 round mags ax unless pre-ban).
Sorry, wish there was better news but that' that. Hope that helped.
Rome