Do points roll over if I don’t spend them all during level up

There is a trick to disabling some of the traps in that area, you probably already found it. This disables enough of the traps that you can cross the area, but not all of them:

Light all the braziers in the adjacent room to disable some of the traps

You should be able to disarm the traps if you select only a single party member and click on them when the mechanics icons appears. I've no idea why this doesn't work in your case. Though I'm not sure if you can disable these specific traps at that point, my character wasn't able to actually disable them.

You can get your party across through the traps by moving each one individually. Just click on the portrait of one of your characters, you'll only move this one then. It's a bit annoying, but possible. There is also another way around the whole thing, so if you don't want to bother, just look for another way out of the cave.

While your companions idle, they will gain a small fraction of experience.

But, once you get the Stronghold unlocked, they will idle there and can eventually (with the proper upgrade to the Stronghold) go on their own side adventures which will grant them additional experience, items, money and even give your party reputation boosts. You can check in on your idle party members to see what they are up to at any given time.

I would recommend going back and exchanging 1-for-1 party member each time you level if you care enough. It is unlikely that the idle members are going to level at the same rate as your main group, so they will still be short of a level. You can finish their level off and more importantly you will be the one selecting their talents and skills for the level-up. If they level while you aren't in control they will choose their own and will often derail any plans you may have had for them or just in general pick some awful options.