Is it OK to change Wire gauge in the middle of a residential circuit?

Good practice would be to run one circuit for the 5-6 outlets on a 20 amp breaker/12 gauge wiring and a 2nd circuit for the lighting on a 15 amp/14 gauge wiring. Outlets can handle large loads like space heaters, etc.. without affecting the lighting ....that way, if you trip the breaker for the outlets, you would still have lighting in rooms. At the very least run one circuit for everything on a 20 amp breaker/12 gauge wiring.

The formula for figuring loads is Amps X Volts = Watts. So a 15 amp breaker at 120 nominal household current/volts will handle 1800 watts of load before tripping the breaker...a 20 amp breaker X 120 V = 2400 watts. The rule of thumb is to reduce the total max load a circuit will see by 20 percent to avoid overheating or tripping issues. So a 15 amp breaker/circuit should only handle 1440 watts max (1800 X 80 percent = 1440)...a 20 amp breaker would be reduced to 1920 watts max. Add up all the potential loads on the circuit from lights, ceiling fan or outlet items and see if it will fall below those threshholds or future use.

If you put all the outlets and ceiling fan/ lighting on one 15 amp circuit, you risk tripping the breaker if all the items in the circuit are on at one time....especially if you have high draw items plugged into outlets like space heaters, hair dryers, vacuum cleaners, window AC units, etc.. Window AC units should have their own dedicated 20 amp breaker / 12 gauge wiring circuit.

You can safely run 12 gauge wiring on a 15 amp breaker/circuit but not vice versa.

You have strange, unorthodox ideas because you aren't trained. You also would be hiding the fact that 14 gauge wires are in the circuit if you ran 12 gauge wires to the circuit breaker. I say you should use ALL 14 gauge wires, and a 15 amp circuit breaker. Very simple.

If you want to change things later, then run metal conduit in the walls. You can pull fatter wires through later, and get rid of the 14 gauge wires and 15 amp circuit.

The purpose of the breaker is to protect the wire, which would be the weakest wire. So a 15 amp breaker and 14 gauge wire. The way I like to do it is use only 20 amp circuits and 12 gage wire. Lights go on one circuit, outlets on a separate circuit and any room always has outlets on 2 circuits (share a common wall). Plenty of outlets convenient to hypothetical furniture, so there are no extension cords or fights with the furniture to plug in a lamp. Being generous always has pay back in not having problems.

yes, it is ok to use 12 gauge wire from the breaker box to the distribution point. And, I'd add a note inside the breaker box that the breaker is limited to 15 amps and may not be swapped out for a 20 amp.

It would be better to run 12 gauge throughout and then use a 20 amp breaker. That's the normal way for outlets these days -- which are usually on a 20 amp circuit just to accommodate that device that includes heating something.

If there is any #14 feeding receptacles then the max size breaker is 15A.

You can use #12 anywhere on a 15A circuit, #14 is just the minimum size.