Hello fellow British penguins fan! I'll do my best.
1.
No, players can only be traded for assets, whether that be players or picks. Or technically nothing depend on conditions on picks or whether a player is just traded for 'future considerations'.
A way the that money can be exchanged between clubs is retaining salary. A team can retain up to 50% of the salary of a player.
A team can get a player from other leagues in various ways, if they drafted them while they were eligible the player can sign a contract to come play with the team before the NHL season. If a player is coming into the league after having begun the season abroad, and with no team owning their rights, then they need to clear waivers in order to join that team. This is not always a given. (1) (2)
If a player can also come to the NHL team that owns their rights after the season of the league they were playing in ends. Also I know in the case of the Swedish Elite League there is a deadline for transfers in season. The Leafs recently exercised this to bring William Nylander (their 2014, 1st round draft pick) to their AHL team.
2.
Do teams sacrifice a season for a likely first round pick, knowing there is a potential superstar available?
Frankly, yes. People believe the Sabres are doing that this year in order to draft McDavid, that Penguins did it for Mario Lemieux and the Ottawa Senators were so blatant about doing it for Daigle that the draft lottery was instituted to try and discourage the practice.
Can a player turn down a team?
Technically? Lindros is the most famous example having done it both at the NHL and at Juniors. It's really rare though. This explains the situation way better than I could
3.
Depends on the team. The Kings are pretty notorious for not caring after having become the first team to win the Stanley cup as and 8th seed and doing so again last year playing only one series with home ice advantage.
Most teams however, prefer to try for a higher seed a) for a better matchup b) for home ice.
Teams with a chance at it do try to win the presidents trophy, but it's not the one they really want(For players, teams and fans alike). It's not unusual for players to get rested towards the very end of the season.
Uh, let me know if you need anything clarified.