Previous owner overheated vehicle, now multiple issues

My vehicle has not had the happiest life. That being said, at some point it overheated and someone just threw the thermostat out. I understand that as long as you use enough antifreeze and do not want hot air it’s sort of okay. The radiator didn’t go bone dry but when I put a new thermostat in it took two gallons to top it off with engine running. Now it has a service light on, however it runs okay, acceleration is not good but it never would put you in your seat. Plus the accelerator pedal is in a weird place. My question is this: is I am taking a beach trip in August, it is a little over 200 miles one way. I know there are millions of variables but generally would it be able to make the trip? I am very familiar with this model and this particular vehicle. It sat for years under my father in laws garage or outside. It has always run eventually. My neighbor “fixed” the ignition by hard-wiring a push button start as long as the key is in accessories (I think). Now the radio loses its memory when I remove the key. And it hollers when you cut it on for a second or two. Like if a buzzer and a male cat had a sound baby. So I don’t know what that is either. Sorry for such a long question, I appreciate any advice or suggestions, and am willing to answer any questions as best to my ability. Thank you, S