The overflow issue is independent of the sticking issue.
When you make a high gravity beer, you can get a really thick krausen. When you make them, you want to stick a hose inside the rubber grommet (for a bucket) or inside the carboy bung (for glass). You stick the other end in a jar of sanitizer. The hose gives the excess krausen a place to go instead of blowing off the top of your bucket or foaming out the airlock.
You want a bigger population of yeast going into a higher gravity beer. If you under pitch, you have too few yeasties working harder than they want to, they get stressed, and go dormant before they are done working.
To get it going again, you want to make a starter that is about the same ABV that you have in the fermentor. You want an active population that is tolerant of the same ABV you are going to put them into, otherwise the new yeast might shock and go dormant too.
Starters are always recommended. If the brew you are doing is over 1.060, they are a necessity.