Yeah, iirc even local stuff is well above $10 for less than a pint. You can't compare costs though; the whole economy and tax system (and therefore 'spending money') is quite different from ours.
My bottles never wanted to carb that fast, but I'd say just work backwards - figure out how long your bottles normally take to carb, add a few days buffer, and leave the rest of the time for primary (no secondary)
It's not likely to ferment in the keg, but I'd still drink it sooner rather than later. You can backsweeten with juice or concentrate to get more apple flavor with the sweetness.
I didn't get an OG on my most recent cider batch (and it was juice I'd never used before; good times) because my hydrometer was at a friend's house. Luckily he recently picked up a refractometer, so hopefully I can grab both and math out the OG.
I messed around with a string in a hydrometer - I used a very light string and it still threw off the readings by quite a bit (the string made it heavier)
I think that skunking would be a concern only later in fermentation when the UV can penetrate further into the [clearer] beer, but that's just a guess without trying to figure out light penetrations vs. srm/cloudiness, so ymmv