Trying to figure out why these two lights are constantly on in the recent weeks.
Get the codes read. At the very least, it will tell you what the car is trying to say. BTW, with the ABS light on, the system is disabled, and will not kick in. This is a part of the fail-safe system. The brakes will work as normal.
That CEL (check engine light) is just a kid in class waving her hand trying to get you attention because she has the answer. You need to have the codes read. Some places will read them for FREE. Try Autozone or Advanced Auto Parts. Get the exact code (like P0123) not just their translation into English and post it back here.
Regarding warning lights:
if the coolant temp light comes on, shut off the engine ASAP
if the oil warning light comes on, shut off the engine ASAP
if a FLASHING MIL/CEL comes on, shut off the engine ASAP
ASAP means driving to the berm of the highway right now and not waiting for the next exit.
But if the MIL/CEL is not flashing, then it’s not an urgent indicator.