the best thing to do is check your fluid level , if that proves ok you could benefit from a road test by a transmission specialist and there no cheap fix to this one you see there are electrical solenoid and module units that operate the box this is a job for a specialist
the reason,s are many sounds like your clutch is not clearing ,check the cable or hydraulics depending what you have , if they are ok you will need a new clutch
check all around the tank area that external wires not mouldy or broken yes you may have a faulty float unit , best bet is to remove the tank and get a auto electrician to check it with a meter it takes little time other than that you will probably need a dash removal
there is a fuse for your fans however if it has blown there is always a reason why , your fan motor could have seized or shorted out , replace the radiator as your mechanic suggested then he will check out the fans a bad cooling system could ruin your motor so it,s best to get it sorted