1) Time compression is not allowed. Possible exception over the Atlantic, but even then, people disconnect, fly their route at 16x or whatever, then reconnect over the coast of Ireland (or wherever their exit point is). In general, if you want to use time compression disconnect then reconnect. Always fly 1x while on VATSIM.
2) Busiest time is usually evenings in each region. Meaning in Europe I'd say around 1800Z (6 pm GMT or so), USA around the same time but Eastern, Central, Mountain, Pacific as you move further west etc)
3) Yes, you need to submit a flight plan. I suppose if you're flying in uncontrolled space you don't *have* to, but it's good practice, not to mention it's fun for people to look you up on ServInfo and see where you're going and how instead of "No Flight Plan filed". That having been said, controllers will ask you for a FP if they don't see one, but will be willing to help, so don't worry. For VFR flights again, file a flight plan, but of course it can contain landmarks etc. (For example "Departure south, then over harbor, Ellis island, around the statue of liberty, north, approach from the west for landing" is an acceptable VFR flight plan. You can leave it blank, but a controller may ask "What are your intentions?" If that happens, answer
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