Can a 20A circuit that trips often be changed to a 30A unit if the attaching wire is at least 10 gauge?

the least count of screw gauge is 0.01mm OR 0.001cms..

Yes you can as long as it is feed off of a 20 amp circuit in at least #12 gauge wire.

(1) Re-wire the fridge circuit and/or the range circuit with larger gauge wire. (2) The range should be on its own circuit already (if not, put it on its own circuit like NEC mandates). You could try running a separate circuit just for the fridge too. You only _need_ to use 14 gauge wire, but use at least 12 gauge wire to help reduce voltage drop. (3) If voltage drop is a problem elsewhere in your house, it might be time to look at a service upgrade.

Certainly. Providing that the circuit is capable of safely carrying 20A. But the circuit was most likely put on a 15A fuse for a reason. ie. the circuit can't handle more than 15A. As a general rule, always replace a fuse with another of the same rating. You need to ensure that all wire in the circuit is at least 12 gauge. This is usually not the case in lighting circuits where the wire gauge is typically 14 gauge. Also all switches and outlets on the circuit should be rated 20 A which is non-standard. If you are replacing the 15 with a 20 because the circuit keeps tripping, that is probably a BAD IDEA.

Least count of micrometer screw gauge is found by dividing the pitch of screw gauge by total number of lines on the circular scale.