A7. Most of the teams keep a "Team House" within about an hour's drive (more or less) of the venue. During the regular season the players live there most of the time. Whether they stay there year round, during the off season, varies from player to player, and team to team.
A8. Typically, no. A lot of that get's placed in the store "vault" (read: taken off the store page) after a season/tournament. You'll keep the icon if you purchased it when available, but you can't buy it once it's gone.
Also, on the bottom end of things, there are some things to know. Unlike in most other traditional sports, where the leagues are pretty static these days (With the most that typically happens is a team moving cities due to new stadiums/city funding/etc, and the rare new team joining a league), LCS is more dynamic.
Like baseball, there's a "minor league" for League Championship Series. This would be the Challenger Series. Like minor league baseball, LCS teams that are short of players for whatever reason, can ask for temporary players to fill in. Echo Fox had do this for most of the early part of this Spring Split, pulling players in from the Challenger team Ember due to visa issues.
Now, here's the catch. Challenger Series (CS) teams, are also competing for the chance to move up to the League Championship Series (LCS). Likewise, you'll hear the term "relegation/relegated" be tossed about for the LCS. This refers to the three last place teams in the LCS at the end of a Split.
So, while the LCS is on going, the CS is playing their own short-season split format. The top 4 Challenger teams from each split, then go on to their Challenger Series Promotion Play Offs. The winner of the CS Play Off, get's the LCS spot of the 10th/Last place team in the LCS Split (AKA, "Auto-Relegated"). The 10th place team, likewise, is demoted to Challenger Series (So basically, they swap spots).
The 2nd and 3rd place teams of the CS Playoffs, then go on to a "Promotions" against the 8th and 9th place teams from the LCS Splits (with the 2nd place CS team choosing which of two LCS teams they wish to play against, the 3rd place team gets the other. Promotions, are Best of 5 battles between these teams, with the winner of each match up getting or keeping an LCS spot.
TL:DR version: 8th and 9th place LCS teams after a Split have to win 3 games against Challenger Teams to stay in the LCS or lose their spot to the Challenger team. The 10th place team, is automatically demoted to Challenger Series, and replaced with a Challenger team