@michee ,Michelle, A little vibration from an engine being felt in steering wheel could be normal. If excessive the engine could be experiencing a misfire and in need of a tune up if it has not been done in a few years or could have a failing sensor. You can have the car scanned to see if codes are being stored for the fault. Some of the auto parts suppliers offer free code reading like Pepboys, Nappa, Advanced auto parts,etc and some of the guys are very knowledgeable and may have seen the issue often and put you on the right track.
Another reason for excessive vibration could be worn/weak/broken engine or transmission mounts(rubber mounts deteriorate over time and can crack and break), a good local repair shop can check this.
As far as you signal lights not working when hot, possible weak failing signal flasher/relay, change out and see if that corrects the issue or have the guy at parts store locate and change for you. Good luck. I hope this helped you out, if so let me know by pressing the helpful button.