Your best bet is to write to the Court or Fixed Penalty Office that issued the tickets. They will be able to tell you whether you have an actual conviction or a fixed penalty. There is a difference between the two. For the nationality application -- and I assume it's the same for ILR -- you *do* have report any traffic convictions, but you *do not* have to report fixed penalties.
If you got done by a speeding camera, it's probably a fixed penalty. I'm not sure what's most likely for the seat-belt matter.
There is a table in the guidance notes for the nationality application that describes the 'rehabilitation' and 'clear' periods required for convictions not to adversely affect your application. I suspect ILR follows similar procedures.
Basically, you should not try to hide anything that you have to report -- be honest and repentant. If you try to hide something, they'll notice it and that will affect you a lot worse than being upfront about it. However, you don't have to report fixed penalties -- they are *not* convictions. So, basically, be rigorous about everything you must report, but don't volunteer any unnecessary information.