I see motorist going through red lights just after they have changed, but not when they have been red for some considerable time as cyclists do and I can't remember see anyone driving on a pavement for more than a few yards.
The "just after they have changed" motorist RLJers are most common, but then you get the ones who keep on going when the lights have well and truly changed but they think they can get away with it before the conflicting traffic gets to them, and there really are a growing number who just drive up to a red light and seem to treat it as a sort of give-way where they check nothing is conflicting and floor it through the junction without waiting for a green light. I notice this last sort mainly when they do it through the green light phase of a cycleway, which they tend not to look for, probably because we usually can't kill them.
Driving along the pavement here is mostly one of three varieties:
1. I'm not waiting for that f#(<ing queuing car ahead wholly/partly in this lane to move before I go straight on / turn left (depending on road layout);
2. I'm not stopping for that f#(<ing emergency vehicle to get past me so I'll keep driving along the pavement at nearly full speed; and
3. parking.
...but I have seen many others, including trying to drive around bus gates or other access restrictions.
I'm surprised you're not seeing these near you yet, but that could be natural variation.
Riding as described above/going through a red light, riding on the pavement are all very deliberate actions. A close pass/pulling out etc are often just crap driving.
Anyone who drives should have demonstrated ability to drive correctly to pass the tests, so crap driving is also a very deliberate action. People cycling on the pavement might be simply ignorant, although that doesn't excuse it or defend against a fine.