Can damaged TARDISes be fixed and aside from flying weird does the damage  cause the TARDIS to function improperly?

Please define "damaged TARDISes", do you mean glitched/bugged TARDISes? or do you mean a damaged looking interior/exterior? all Tardis' should work and fly the same regardless of interior/exterior as long as the still have a demat lever, a monitor and perhaps a flight pannel unless they are as mentioned glitched/bugged.