You will need to exchange your UK DL in 6 month max. This is in case you become a permanent resident. If you leave the country within 6 month I would not worry at all. Don't let police make you grease their palm. By law you can drive up to 6 month with an International DL.
Regarding tires, as far as I know no one check the tires in summer. Only problem is when the winter season comes the police does check the tires to make sure their are for winter season.
If you don't need to travel long distances( up to 10-15km a day), the best way to move around would be a bicycle - just avoid high traffic road.
Ask anything you have on your mind. I am located in Nisporeni. Will help to the best of my abilities. Cheers.