I've got some Hidersine pegdope - recommended to me by an ex cellist - but my teacher says graphite pencils are just as good. She uses Wittner geared pegs, however. I assume the idea is just to push the pegs in harder if they slip, and the dope makes turning them smoother, but I'll try to remember to ask that question explicitly.
I asked it. She said good pegs don't slip. Pushing them in harder may be second best to buying a good violin, otoh she'd never seen a pegbox fail as a result of pushing pegs in. Good pegs don't slip? Presumably, though, you still have to push them in hard enough first, however hard that is!
For the pegs to work properly they need to be fitted properly. The quality (within reason) of the pegs and the violin doesn't matter. It's all down to the skill of the person who fits them. The way the string is wound onto the peg can also have a surprisingly big effect on how well the peg works.
Regarding new instruments changing with time, we generally find they get better with playing. There's also an effect due to the player getting more used to the instrument with time. However, it's very common for the sound of a brand new or newly restored instrument to deteriorate as the shape changes ever so slightly with string tension over time. This is because the sound post no longer fits well (a change of only a fraction of a millimetre can have this effect). So if your new instrument starts to sound worse, don't think you've bought a dud - take it back to the shop or maker for a new post.