1. There is no way of fully guaranteeing that one does not get 'bumped' out of one's seat but what you can do is check regularly that your seats are still there, particularly if there is any announced equipment change etc. You are also less likely to be bumped from seats further back as in the case of equipment change or cabin modification, seats close to the front are the most likely to 'disappear'.

2. What you should do now is (1) Check in online as early as possible (30 hours before the flight from most destinations, 24 hours for a few). Not all seats are available to pre-assign so you may find that there are still four seats together when you check in. (2) if OLCI didn't sort your problem out, try and go to the airport early and again, ask at the check in desk. They may be able to have access to some seats which you can't access directly. (3) if that fails too, indeed, do speak to the gate agent, but by that time solutions are less likely to be available although of course, they may occur if some people don't show up.

3. It depends how you ask and what you have to offer. For example, if you ask the person on an aisle seat to switch to a middle seat, then yes it is rude. However, if you offer a swap aisle for aisle especially if the new seat would be further forward (which many people prefer) then it is certainly fine asking nicely explaining the situation and being profusely apologetic/thankful. Of course, it is not guaranteed to work: the person in the fourth seat might be travelling with someone across the aisle or simply not want to change for whatever reason, I think that if they say no you shouldn't insist, but if you are comfortable with the fact that the seat you are proposing them is as good/better then no harm in asking

4. Again, no you don't get compensation for that sort of issue and if you have an extra bag you can be certain that they will make you pay for it.