1) We know Warp Time Travel is possible, with no noticeable aging effects (like Lysander), but I don't think we've seen 10k years of it. Lysander was only about 1,000 years.
2) It would be a cool touch, you could use them as veterans (or normal Marines, your pick). Fluff Murder? Possibly, some of the more zealous chapters may kill them since they might be "tainted". Not too up-to-date on
BA stuff.
3) If I remember the bit from Lysander, it didn't have a whole lot of an effect. Most of his damage came from the fact he reappeared surrounded by his Chapters most hated enemies (and his was unarmed.). He still showed an equal amount of strength for a Space Marine Captain, however.
4) Most likely destroyed by the Inquisition if it was for too long (Lysander lived because he slaughtered a ton of Chaos followers just after getting out, proving loyalty). Depending on how close the chapter was to the Inqui, they may just fold back in quietly.
Hope I could be of some use, and if anyone else comes along saying something different fluff wise then I did, believe them. It's been a little while