You should look up the meanings of 仕方, maybe your interpretation “way” is too literal. It means a way (to do things), a method, how to (do) things. (仕 puts emphasis on actually doing something.) So it could mean “[there] is no way to do [this]” or “can’t be done”.
yes. here “ga” is a particle. there are some vocabs that are common phrases and include particles. shikata ga nai is one of them. Some other examples of this are
興味がない(きょうみがない)no interest (from level 34)
紛れもない(まぎれもない)certain (from level 46)
いい加減にしろ(いいかげんにしろ)cut it out (from level 21)