Using a Carboy That is too Large...

If all you can find is a 6.5 gallon carboy, but you want to make only 5 gal of cider at a time, is the extra space in the top of the bucket an issue due to aeration, or is it simply pushed out soon after fermentation begins? Which leads me to another question: when brewing beer, people often set up the whole blow-off apparatus, why not just use a carboy that is too large so the krausen isn't forced out but is simply all contained inside the carboy?

You should be fine with that headspace as the CO2 will push out any oxygen that is there. And for using a bucket - I think the consensus is that if your brew wants to overflow with krausen its going to regardless of the vessel that its contained in. (So a blowoff tube is necessary either way) Most people use buckets as they are much cheaper and easier to move if necessary.
-Me

Using a 6.5 gal carboy is fine for primary, but you want to minimize headspace once you go to secondary, or once the bulk of the vigorous fermentation is complete. And using a large primary is not only beneficial to prevent the need for blowoff, but also you can put in 5.5 or so gallons in primary and then you are able to rack to secondary with a full 5 gal. without having to worry about topping off your racking losses.