Carbonating

I have a cider I started back in mid December. It has been sitting in a 3 gal carboy secondary for about 6 weeks. It is clear and I would like to bottle it. I want to back sweeten with apple concentrate to add to the flavor and then carbonate.

So I have 3 questions:

1. If it is in a 3 gallon carboy will it be okay going into a 5 gallon keg? (I am thinking the Co2 will prevent oxygen from being in there)

2. If I want to carbonate with a beer gun from the keg to bottles do I carbonate in the keg or only when it leaves the keg to go to the bottles?

3. In everything I have read exposing the cider to air is not good and yet I see suggested DIY filtration systems that cause exposure to air - how is that ok?

1. That's one of the advantages of kegs over carboys. Size doesn't matter. I pull the pressure relief ring a few times while pressurizing to get most of the oxygen out.

2. Carbonate in the keg. I don't own a beer gun, but it is my understanding that they are for filling bottles with previously carbonated beverages. They don't carbonate them.

3. I don't know what filtration systems you are referring to, so I can't comment. Short term exposure to air isn't bad. Long term exposure is bad and so is agitating the cider to introduce air post fermentation.

Since you are backsweetening with concentrate, I hope you're doing something to avoid refermentation by adding sulfites and sorbate, constant refrigeration, pasteurization, etc.

Yes, I plan on stopping the fermentation before adding the concentrate.