A brand-new guitar will be tough to keep in tune until the strings get stretched and settle in. The best way I've found to accelerate the process is to
slide a finger beneath each string about halfway up its length and give it a tug (gently!), then re-tune. Repeat this several times until it starts holding tune. You'll still need to periodically re-tune (as with all guitars), but it won't be near as bad as it is right now.
As to your problem with fret buzz, it could be a number of things. Start off by reading UGB's "Buzz!" thread, which is pinned at the top of this forum - he gives excellent tips on how to fix the problem.
