Yes but there are two stipulations, one that the join or splice must be made in a junction box that is accessible and has a removable cover and the second stipulation is that the breaker that is supplying the power can not be larger that the smallest conductor. In this case no breaker larger that a 20 amp breaker as #12 wire is only rated at 20 amps..
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Yes as long as the circuit breaker or fuse that is protecting the circuit is of the ampacity of the smallest size wire. In this case it would be the #12 wire which has an ampacity of 20 amps.
12 gauge underground wire or if you think you will ever add any devices to this circuit use 10 gauge.
No, 10 gauge wire requires the use of a 30 amp breaker. A 20 amp breaker is only used on 12 gauge wire.
10 AWG should never carry more than 30 Amps.
You can pull 10 #3 gauge wires in a 2 1/2" conduit.
In the United States and according to the NEC, in commercial and industrial installations, you are limited to 10 receptacles on a 15 amp circuit. The size of the wire is not a determining factor. There is no limit to the number of receptacles on a circuit in a home and there may be local codes where you live that have stricter requirements.