1. PSK or cshea will probably know better, but if you sign him now, he can go on LTIR and his cap hit is off the books until he’s back. As far as what I think you’re asking, the Ruotsalainen Rule, which kept teams from having wink-wink nudge-nudge deals with overseas players, wouldn’t apply here
2. Again, willing to be corrected, but I think the playoff eligibility cutoff is the trade deadline, and Rask should be recovered well before it.
3. He’s said he’ll only play for the Bruins, so you wouldn’t think so.
All that said, leaving him unsigned means he rehabs completely independently of the team, and you do run the risk of pissing him off to the point he retires and goes home to Finland. Honestly, the better play would be to sign him after the expansion draft, stash him in LTIR-land, and worry about him infringing on Swayman or Vladar when the time comes. As good as both were this season, I’d like to see more than a third of a season’s work before handing the reins to them full-time.