You seem to be on the right track.

Couple of questions.

1. Is 2 singers all you ever want to be able to support?

2. I see you have the mackie 12 (great speaker) but only the Rockville 10s. Honestly either will work for your space just be sure your comparing apples to apples. So for the question will you be doing anything else with the PA? If it’s just for karaoke Bluetooth is just an expense you won’t use. If you are ordering from Amazon I’d start with the Rockville’s try it and if you’re happy with it great if not return them and get the mackie.

Now to answer a couple of yours.

1. You do not strictly speaking need a mixer. If you go with the first mic Set it appears to have only 1/4 trs output so it would be important to make sure the speaker you get either has that input or get a cable that does 1/4 trs to xlr. The second set looks to have both I went with a different set of mics and have been happy with them they also have the ability to change volume per mic and can output to trs (all mics no mixer needed) or xlr (each mic individually mixer required).

https://www.amazon.com/gp/aw/d/B0B3MMP1NJ?psc=1&ref=ppx_pop_mob_b_asin_title

Reverb etc is nice but you may want to start with no Mixer and see what you think then you can always add one later.

1. Since you’re going with an Apple TV you should try out a week pass for KaraFun the KaraFun app is really slick and has a ton of songs it’s 7/mo and I think either free or just a few dollars to try for a week.

2. Your cable assessment is correct assuming you go with that mixer.