Re: Does a fluted barrel effect accuracy
Not that I've heard of, although theoretically because it reduces mass, it should reduce rigidity. Having said that, a lot of folks back when I shot BR would have their barrels fluted to make weight and BR shooters would do NOTHING to impair accuracy.
Re: Does a fluted barrel effect the amount of rounds a barrel can handle before needing to be replaced
It depends. The fluting will keep the barrel cooler longer as there is more surface area from which to dissipate heat, but if you continually fire a bunch of rounds in a high performance calibre, you're going to burn out the throat regardless of fluting. ie. .223 WSSM vs. .222 or .22 Hornet, or .300 RUM vs. .308 Winchester, a 7STW vs. a 7x57 or 7mm-08.
Re: I want a rifle I can shoot a lot of rounds through without worrying about it getting too hot but I also want to have as light of a rifle as possible.
Then get a mountain rifle contour in a lower intensity cartridge & space out your shots, especially in +30 weather in the summer.
Just my $0.02.