#1
On a LP that I use mainly for standard, will dropping it to D-Standard for a few days at a time (and doing this fairly regularly) warp the neck? I always played between standard and a half step down on my Martin, but that's a whole different ball game.

Also, would beefy slinky strings work okay for these tunnings? I usually play power slinkys but I still have some excessive buzz when playing hard... After months of trouble shooting the only real possible reason left is that the neck doesn't have a lot of relief (truss rod zeroed out, I got about 8 hundredths relief). Action is decently high too.
#2
No, it won't warp your neck. As always, check the truss rod occasionally to see if it needs adjustment.

The key is setup, the gauge is obviously a factor but D standard is close enough to E that once set up properly you should be able to switch between them with few or no issues. A super straight truss rod might be contributing to the buzz, although it would be smart to have someone check the frets to see if they need a level/crown/polish too. A little buzz is ok if it doesn't come through the amp.
#3
Nope, it won't warp the neck and yep, those strings should be fine. I go from E standard to 'totla mad' tuning (A♯, G, C, F, A, D) on my Explorer (because I'm that cool) with a D'Addario 11-56 set, so you should be absolutely fine
#4
Nope.

Yep.
Charvel DX-1 FR / DS-1 ST / DC-1 FR / Custom Strat / La Patrie Hybrid CW / Vypyr 30 / VK100 / 1960A