Not necessarily. They are more fixed on the PP. If a team is losing late then it's common for the best D and fwds to be out more.
Depends on the coach though. An incompetent staff like Joe Sacco and his assistants on Colorado don't plan matchups correctly or they just pick names from a hat.
Depends what you mean by "routinely". It does happen sometimes, but not as a rule.
Usually it's more match-up based than anything. Say the Bruins are playing the Penguins, you might see Bergeron and Chara matched up with Crosby all night. That being the case, Bergeron's line and Chara's pairing will be together for the most part.
In Norh America not necessarily. The old russian tradition is to play 5-man units due to emphasis on puck posession and passing play in russian hockey.
Kinda common in Sweden, but as opposed to the NHL, you're allowed to dress 20 skaters and 2 goalies, which gives the opportunity to roll four complete units.