Recommendations for beginner kit for Cider from Apples

Sounds perfect. The airlock is not an any-way essential part of the process, so don't worry at all about how it's set up, nor the lack of bubbles through it. Give it at least a week before touching it and then take a gravity reading.

The hard work is in juicing the apples. Once you have juice, making cider is dead easy: add your juice (cloudy, if store-bought) to a sanitised food-grade vessel, add yeast (a sachet of champagne yeast is best, but any viable yeast will work) and leave it to ferment. In about 4-6 weeks, that'll be cider, albeit flat and very dry. I find it needs to be bottled for three months after that before it's drinkable, and is best after six.

There are good contaminants and bad contaminants. The wild yeast on your apples is grand, but you don't want it out-competed by whatever lives in the scratches in your fermenter, biding its time.

You need to take more hydrometer readings: they're the only way to tell if fermentation has stopped. Bubbles and gas pressure don't mean anything useful, and the lid's only purpose is to stop things falling in when you're not looking — it doesn't prevent infections or oxidation. Since it's pretty clear that fermentation has been happening, you're at much less risk of picking up an infection now than at the start. Take a series of gravity readings using sanitised equipment about two or three days apart, and if you get three readings the same in a row, you can be confident that fermentation is done.

Re racking to secondary: why are you planning to do that? There's a risk of oxidation, so what benefit are you hoping to get from it?

You do not need to fill the fermenter to the brim. Adding more apple juice would restart fermentation, stretching the process out and rendering your gravity readings useless.

If it were me, I would ensure that fermentation has stopped via gravity readings, batch prime it, bottle it and leave it alone for six months.

There's a vast amount of nonsense and bad advice about home brewing out there, so always ask what something is for. Knowing the principles behind the process will help you when and if something goes wrong and you have to improvise.

Yes, you will get rid of that lees if you siphon to secondary, but then new lees will form in that vessel too. And new lees will also form in the bottles. Don't fear the lees, just be careful when siphoning and serving. If you batch prime, you'll be leaving the lees behind when you rack to your bottling bucket, and then you won't get any gunk in the bottles. That renders the secondary stage unnecessary, while still making use of your second bucket.

I used to always do a secondary with hop-forward pale ales, because I didn't want the lees interfering with the hop flavour. But after several batches I found it wasn't making any positive difference.

To batch prime, sanitise your second bucket, add in your sugar solution, and then siphon the cider on top of it, leaving the lees behind. There are lots of priming sugar calculators online for working out how much sugar you need.