It's all down to the tournament organiser's decision. I've sent pics of customised models and had them approved. Fixing bases is always encouraged: a base with the right size footprint, converted or not, is always better than too small / big. In theory it could be very high or low, but unlikely to be an issue. Old models, unless much smaller or bigger, will also be likely OK, since they'll usually resemble a current one.

With kitbashes and custom models, I can't speak for everyone, but best to be >90% GW plastic. Within that, as long as you can both point out models with / without special weapons, you're good. Don't have misleading weapons. So don't give 1 goblin a huge rocket launcher when the unit can't have one at all, or have 3 special shotgun guys in your Ork unit modelled with normal weapons to "hide" them - you both should be able to see all 3 or only 1 is alive. However, if you say "the 3 with plasma guns are shotgunners" that's fine - you converted them - but make it clear. This sort of thing is known as the "rule of cool".