I've purchased a house with an outside outlet about 100 feet from the house. It is a GFCI, wired with 10 AWG outside rated wire (I assume because of the distance), run through conduit underground to the basement, where it ends at a 20 amp breaker. Inside the basement, there is a 12 AWG circuit that serves a nearby outside outlet on the deck, tapped into the 10 AWG wire inside a box. It all looks good, but question 1 is: Is it legit to tap into the 10 AWG wire with 12 AWG to serve nearby outside outlet? If so, can I tap another 12 AWG wire into the box to add another nearby outside outlet? (I would probably use WAGO flat connectors rather than try to twist two 10 AWG and two 12 AWG wires together.). Thanks in advance!
Mixing wire sizes is OK as long as the overcurrent protection is sized to the minimum sized wire.
None of the outlets you described seem to be circuits that require dedicated circuits so adding a receptacle tap should not be a problem. You may have box fill issues, each #10 requires 2.50 cu in, and each #12 requires 2.25 cu in, all grounds count as one of the largest size, and if there is a device mounted in the box it counts as two wires.