A) Borked beyond all recognition. While we try to have coherent explanations where possible, in some cases you just have to suspend disbelief - sometimes quite a bit. That's the price you pay to have a place like this work.
A) Short answer - yes and no.
Basically the way the Multiverse works is, the Custodians, or whatever system they use, relies on the theory that everything that can happen does happen. So what they do is they go in on a quantum level and add in a new possibility - a possibility that the entire world or just a person or anything in between suddenly exists in the Multiverse. As such, yes, another them exists in their 'own world' - however, they also exist in the Multiverse. Both have an equal claim to being the 'true' version of that person.
That said, this is why it's impossible to "go home" - home came with you.
A) ICly, it's supposed to be extremely rare that an individual or small group of individuals gets unified without their world coming with them. OOCly, it's less so, because people seem to like to RP coming in alone, or that they find their world later. We generally don't police this.
A) Long technical story is that the Multiverse's atmosphere consists of a quantum-unstable oxygen-based mixture which literally condenses possibility down to whatever's needed. In short, the gas in the atmosphere turns to whatever breathing gas is necessary. This does not, however, help when there's no gas whatsoever, i.e. underwater.
A) Long story short - nobody ages after a certain point. They shouldn't really age, they shouldn't refer to themselves as being a 'year older'. Birthdays should probably be avoided too. However, this doesn't always work out in IC play. The reason for this is OOCly because the MUSH likely wouldn't work out all that well with aging. A group of teenage heros becoming teenage twenty-somethings often loses it's appeal. And do you really want to see Picard get even older, or Sisko, or Solid Snake? Most don't. This makes it much easier. While it does remove some realism and arguably makes some kinds of character growth harder, overall it has a better effect. That said some subthemes do allow aging; these are however extremely ICly unusual.
In terms of science, time simply flows at an unpredictable "rate". Clocks are hard to keep in sync, for instance, and some chemical reactions might take different amounts of time than they should. This is particularly so around beings which are alive, i.e. characters. The existing system is there as a kludge; it works very well, but it's not a true indicator of time as we know it IRL. Time tends to be a fundamentally different beast here. The exact explanations, however, will probably have to wait several hundred years for a more sophisticated understanding of temporal physics to be developed. I hope you have a book to read...