the strips that hold the brass tubes that are closest to the edges.
OK, I believe you are talking about what would commonly be called the side bridges, and yes, they can be glued down. However, they have
to be straight before you glue them down or else you will have the devils own time getting it properly tuned later.
In regards to the string hitch pins, the suggestions to pull the pins and fill the holes with a tight fitting hardwood dowel are good. But instead of trying to redrill in exactly the same place, or drill new holes completely clear of the old ones, you can also do this: Move the center line of the new hole to the outer edge of the existing one. This will result in leaving a small crescent shaped piece of hard wood in place which will act to reinforce the side of the hole that gets the most pressure. This is often the method used on harps where the string is coming up through a soft wood sound board or when a string hitch pin gets damaged on the neck.