That first question has an interesting answer; apps close in about eighteen hours as we enter the finale for season one. A few weeks after that, season two starts, which involves the reincarnates traveling to other places around the world. One easy answer, then, is to send a character wherever the person you're looking to not hear from isn't - out traveling or staying in Locke City, whichever applies. Plot will continue to happen in Locke City even after it also comes calling in other places, so that's definitely an option. That said, there are plenty of characters, and several posts a day; if you'd rather not hear from someone, there are a lot of other places to turn, and we run plot posts every few weeks to start drawing up plans and create tagging opportunities.

As for the second, that's largely up to how much you want to get a character involved. If you get out there a lot, canon recurrences can give you Echoes very rapidly, and if it's things that your old character did or thought, you can cause a very sharp shift in just a little bit of time. Say you played a character that wasn't fond of magical girls for whatever reason. We've got plenty, and they're pretty easy to find - seeing one do something and your character having a strong opinion on it, or even talking to one, could feasibly be enough to shake an Echo loose. Failing that, plot events drop Echoes that let you choose what is returned much more liberally. So if you take things slow, it could be a few months, or more; if you rush through things, you can return a character's personality bit-by-bit in relatively short order. Maybe a month or two? It depends on how many complex facets are going to need to come back. That said, you don't need to take away all the canon personality elements from the character - just the ones that can't fit a modern-day Earth setting (hates vampires, say), and maybe a few more to give the character flavor and make it interesting when those traits come back.

I hope those are useful answers?