Can push in connectors be used for parallel circuits?

"old yellow cap twists" - if you hate the things then use something else.

However you should hate the old ones. Old wire-nuts aren't very good, or to be more precise, newer ones are better designed. I throw away all old wire nuts especially Scotchloks.

The other reason to hate wire-nuts is if you have not learned proper technique. If they don't firmly hold together by themselves, you're not tightening them enough, or wrong-size nut for that many wires. I stock yellow and red, that covers just about everything.

Never, ever tape wire nuts. Or to be more precise, never need to tape wire nuts. A proper splice must easily pass a "pull test" (hold nut, yank each wire one at a time).

"Backstab" connections on receptacles and switches are known to be unreliable. Some here will vouch for the stabby splice, but keep in mind those "came free with the lights" which isn't the highest recommendation in the world.

As long as you connect white to white and black to black you will have a parallel circuit.

only thing to watch out for is how many lights you string together. your circuit may already be overloaded.

if you have about 12 to 16 lights on a circuit you should not add anymore.