Question 1: If Law uses shambles to switch lets say Doffy with Bellamy, and Luffy kills Bellamy, does that mean that Doffy is going to die and Bellamy is going to survive in Doffy's body?
Question 2: If Law uses his shambles to switch again Doffy with Bellamy and Bellamy's body is then turned to a toy what would happen?
Answer 1: So far, the soul seems to be affected as well when the body it resides within is hurt. My guess is this, let's say we put aside the tier list or anything regard to it, then Doffy dies due to the damage of Bellamy's body received from Luffy's attack. Doffy's soul goes up, and Bellamy's body can't be used to put back that Bellamy's soul anymore. Hence, he may survive just being in Doffy's body.
Answer 2: ....err a bit hard to make an assumption of this, since it's not really confirmed in more details about the toy-change stuff. But i think Sugar's power has a great effect on one's mind & soul, so even if the body is switched, the important matter is whose soul in that particular body. Thus, i believe people will forget about Doffy as he's in Bellamy's toy body.
Have been answered above

Thanks, LitzSabr
And what are some common abbreviations or general terms that OP fans regularly use?
Here some:
NW = New World
GL = Grandline
DD = Donquixote Doflamingo
WB = Whitebeard
BB = Blackbeard
CD = Celestial Dragon
WG = World Government
EOS = End of Series
TS = Time Skip
M3 = Monster Trio (Luffy, Zoro, Sanji)
ID = Impel Down
MF = Marineford
FI = Fishmen Island
SH = Strawhats (Luffy's crews)