As long as they aren't oversized bars, they would work for IHC, but you'll need to drill the starnut out of the bars or push it far up into the bars. Be very careful if you decide to drill it out.

Yes, you can cut bars down, but there are a few things you need to know. First, if it has a slit in the bars, that slit needs to be recreated after cutting the bars shorter. The slit should be in the same spot and the same width and length. Second, if your bars have a starnut inside the bars, such as for ICS, it will need to be pushed further up into the bars equivalent to the amount you cut off.

The Grit Fluxx comes with a non-integrated headset (it looks like some might even be threaded, which I would argue is not HIC). Integrated headsets should be interchangeable, but I don't know if non-integrated headsets are. They might work, but you should try it out before buying. It's definitely not integrated though.

It might work, but it also might slip from side to side, not staying straight because there is nothing holding it in place other than the one bolt. Some Phoenix brakes had only one bolt, but they had tabs that held them straight within the deck. The best advice is to buy the right brake for your deck.

Standard diameter bars will work with IHC, but the need a slit.

Apex Bol bars come in standard or oversized, so you can stay with oversized bars. If you want to go to standard diameter bars, you'll have to change your compression system from HIC to SCS or IHC.