We're putting in a new dishwasher that will not be located directly next to the sink. It's on the other side of the room under what will be a new countertop. The plan is to drain the dishwasher through the floor into the crawlspace and tie it directly into the 2" horizontal drain line that serves the kitchen sink.

The current thought is to drop a 1.5" line vertically through the floor into the crawlspace, install a p-trap, then run it horizonatlly over to the 2" line. My questions are as follows and any clarification would be appreciated.

1) My instructions say I need at least 18" loop or an air gap in order for the dishwasher to operate properly. Is this only if I'm draining "upwards" to the sink, or do I still need that when draining straight down to the drain in the crawlspace? Since the DW drain will be tied to the kitchen sink drain far downstream of the sink p-trap, do I really need to be concerned about a clog backing up water into the DW? If not, then why do I need an air gap?

As I understand it, the air gap prevents reverse siphoning so that a clog in the drain will not back up dirty water into the DW. But since I probably won't have to worry about a clog on a 2" line from the DW waste (the DW drain hose is only 5/8" dia, so if stuff can make it through there...)?

2) And now for the drain vent. To simplify the drain vent runs, my plan was to put an air admittance valve (Studor valve) in the crawlspace tied in with the horizontal portion of the DW drain line, but others have said I need to vent the drain to the roof. Is there an issue with putting an AAV in a crawlspace? Any suggestions?