No you wont need to isolate the studs.
I would get some cavity fixings to hold the timber studs to the existing wall.
Drill say 4 holes in each of the upright timber studs (one top , one bottom, two inbetween) not too big say with a 1/8 drill bit.
Next postition the timber stud where it needs to go all leveled up. Then with your drill, drill though each of the holes in the stud just enough for the drill bit to exit the rear of the stud and make a mark on the existing plasterboard wall. Repeat this process for each stud.
When you've done that get your cavity fixing and as you can see on the head of it (ignore the screw for a minute) it has a star shaped slot which is for your screwdriver or cordless drill if you have one.
Find the marks you've just made on the existing wall and screw the cavity fixing into the plasterboard, it's corkscrewed as you can see so will drive straight in.
**When purchasing the cavity fixings they dont need to be too long because you dont want to be hitting your breezeblecks behind i'd say go for some 20mm cavity fixings)
Once you have all your cavity fixings in you can fix each stud to the wall one by one. Just stand it back in where you had it before and use the screw provided to fix it. The screw will go through your previously drilled hole in the timber stud and enter the cavity fixing and will do up nice and tight
**If when your fixing the cavity fixing into the existing wall you hit a pit of the board adhsive holding the exisintg plasterboard to the wall dont panic , just drill a new hole in the stud a bit higher or lower than the one you just did.
Cavity fixings dont cost a lot and can be bought at any d.i.y shop.
I cant pass comment on the "air gap" for imporved sound proofing i'm afraid, i cant say if this is true or not.
It's not necessary to fix the uprights to the top and bottom timbers just cut them in between (to be honest if you're going the timber route you dont really need them but it wont hurt to put them in)
"Someone mentioned that soundproofing may subject to the 'Party Wall Act'. Is the true?"
lolol i dont know about that one but it sounds very much like someones having a joke with you lolol
hope this helps
Jon