PSI of naturally carbed cider? (First time kegging with a bottling question also.)

[Garfield43]

Hello, my homebrewing odyssey continues.
I make cider using store bought apple juice and DADY. It works fine and I haven't had any problems but so far I have just been brewing in the bottles the apple juice comes in.
Currently I have a bunch of cider in the jugs the apple juice came in.
It has been chilling out in the fridge after fermenting for a month or so.
My plan is to transfer it to my keg that has a floating dip tube, after sweeten it with concentrated apple juice and let it naturally carbonate at August room temp.
I have a pressure gauge hooked to a quick disconnect.
What PSI should a reasonably carbed cider be?
I don't want it to be like champagne, just have a little fizz.
I have found the carbonation really seems to effect the flavor.
Also would it hurt anything to run the cider through a coffee filter as I put it in the keg?
Many people say that will turn my cider in to vinegar.
Is that true?
My plan is to put my cider and some concentrated apple juice in my keg let it set at August room temp until it has carbonated than move it to the fridge.

I think I have more than will fit in my keg so this brings up bottling.
I have some flip tops.
Does anyone just run them through the dishwasher with no detergent and call them sterile?
My dishwasher has a water heater and gets good and hot.
I don't know for sure if it sterilizes.
Was just curious if any one else called this "good enough" and what results did they have.
Did their brew turn out ok?
Did they die?

Thanks for any and all replies!

 

[Yooper]

DON'T pour it through a coffee filter! You'll ruin (oxidize) the cider. Siphon it gently without splashing from off of any sediment into the keg.

No way to know how much carbonation you have right now. It depends on temperature, the amount of sugars that were originally present, and when you capped it. If it's spritzy enough now, you can try racking (siphoning) it into a priming sugar solution (or your sweetener) so that what c02 you lose when racking you can recoup when the sugar ferments in the closed keg.

To sanitize the keg and bottles, you can simply use a sanitizer solution, and it should also be used on all of the equipment.

Turning the cider into vinegar requires a bacteria called acetobacter, which you can get from unsanitized equipment.