And hot at lower elevations where there is more pressure?

From what I understand, warm air rises because the air molecules are more spread apart and this makes the air lighter. Cold air is more dense and sinks. So why at high elevations up in the mountains where the air is less dense and there are less air molecules is it colder?

Also, can anyone explain why low pressure creates warm weather and storms and high pressure creates cool clear weather? This doesn’t make sense to me. Thank you!
okay, i guess that makes sense

the only thing i still dont get is if the air is colder at higher elevations, why is there less air pressure? if cold air is more dense shouldnt the pressure be higher?