First Cider, just need some general advice

I got 4 gallons of pure apple cider from king stoopids (nothing added), 1.5 lbs brown sugar, and some cinnamon sticks. I used champagne yeast and nutrients along with pectic acid. It was been in the primary for about a week now. OG 1.056, it has made it's way to almost exactly 1.00 today. I added a Apple Mango frozen concentrate just now and plan on bottling later today. Will it mix itself enough without being stirred? I don't want to mix it up and mess with the yeast. I plan on pasteurizing within the week to taste (I have potassium metabisulphate, but decided against it). I am sipping on a glass now, seems decently potent, look forward to it soon. Is it the same formula as beer to calculate ABV? This is my first post, this community seems awesome.

Hi there I have just checked my first cider I added a clear apple concentrate after Cider was ready to bottle and stirred it in then left it for 2 days to settle again after being bottled and left for 2 weeks the Cider appears to be crystal clear and has very little(almost none) sediment.
Anyhow I am no expert on Cider as I said this is my first (second is in the barrel brewing now) but that is what I have experienced so far .

Okay nice, im debating bottling today or mixing and give it a few more days. I suppose mixing would be better

Here's my recipe

5 gallons of pasteurized apple juice from the store
1 packet of yeast
1 week in primary
1 week in secondary
Siphon into keg, add 1 can of apple concentrate and 1 pound of brown sugar. Close keg and shake for 2-3 minutes. Then taste and add more concentrate and sugar if you want for taste. I usually end with 2 cans of concentrate and just under 2 pounds of brown sugar for a 5 gallon batch, but I like it sweeter than most. It's pretty close to woodchuck after its forced carbonated. I have also used apple, strawberry, kiwi juice concentrate cans with good results. Pretty much just alcoholic juice at that point.
I know this didn't really answer your questions but hopefully it helps.

i would think that it would not mix itself very well, but that your champagne yeast is going to make short work of the concentrate regardless. i would not have added that until bottling time, once i had racked the cider off the yeast. is this still in your primary fermentation vessel? how clear is it, or how actively is it fermenting the new sugar?
if pasteurizing of course you can bottle at any time but if you bottle during active fermentation you are going to have a lot of pressure in the bottle really quickly, and then a lot of dead yeast to avoid when pouring