Music/Lyrics - I don't have any experience with Apple Sing

PA Speakers - in addition to those speakers you also might want to consider this Alto

https://www.amazon.com/Alto-Professional-TS410-Bluetooth-Loudspeaker/dp/B0B9ZP6D61

The Rockville will work, I have one, but it's more of an entry level speaker. IMO speakers with a 10" size woofer is the sweet spot for your situation. Once you go to something with a 12" woofer, the size and weight of the cabinet gets substantial. You won't get quite as much low end with a smaller woofer but if it will primarily be used for vocals you don't need more low end.

Mics:

If you use the Fifine mics you don't absolutely need a separate mixer. But the Fifine is an entry level system. I prefer the Innopow mics.

Mixer??

The Pyle mixer would be a better choice for 2 mics. It has all the features you would need.

Connections/Cables:

Two XLR cables from the Innopow to the Pyle.

If you're only using the speaker for vocals you would need one unbalanced 1/4" cable from the Pyle Main Out (either R or L) to the speaker. Inputs 1 and 2 are sent to both L and R Main Out on the Pyle

To connect the stereo karaoke music to the Pyle you'll need two unbalanced 1/4" cables to channel 3/4 on the Pyle. You will also need a 2nd unbalanced 1/4" cable to connect both the L and R Main Out on the Pyle to the inputs on the speaker(s). If you don't connect both the L and R Main Outputs on Pyle to the speaker(s) you'll only get 1/2 of the karaoke music. Ch 3 input on the Pyle only comes out the L Main Out and Ch 4 input comes out the R Main Out.