Tyres - depends on make and model of tyre and aircraft really. Many modern tyres can have significant (to pilots!) tread damage but be totally acceptable in engineering terms. Damage to the sidewall of the tyre however must be treated with great caution. Your local friendly engineer shoud be able to give a lead.
As regards the fuel guage - probably dependes on type of aircraft and the fuel system, but the MMEL (if you have one for your type) would have the definitive despatch answer. It could give all sorts of problems, not least of all, refuelling correctly.