dash lights that stay on when there is no problem in said system

You may have a bad tire sensor or two. A tire shop can check that out for you. The brake light could be a wiring issue so a hands-on electrical inspection is needed. If you don't normally work on cars, use this link to find a good shop near you. https://repairpal.com/repair-shops Alex

Malfunctioning 'park brake' on/off switch is likely culprit for constant brake light .. TPMS can be recalibrated using button under dash. Look in the owners manual !