Carb problems and more
 

So I'm having problems getting the F2 I bought last summer to be ride able. Let's start with the carbs. When I got it the throttle would stick. Took off the carbs and cleaned them. In the process I had to replace the jets. Also bought new cables as the old ones were frayed. They still stick along with the choke cable but we will get there. They move freely when off the bike so tell me if they are routed correct.
So, the next problem is the choke cable. It sticks and doesn't really want to move the choke bar. I lubed it up loosened the screws. checked the housing which was broke. Bought an "new" one off eBay which is missing the pin to keep it from spinning but it still doesn't want to move freely.
Third and hopefully the last problem is the air cleaner housing. This bike has had a mish mash of F2, F3, and late model F3 parts on it from the beginning. It appears the housing that was on it was from an F3 and the air box never sat right on it and never sealed properly or even fit on the bike right. So I bought a "new" one off eBay hoping it would work as I checked the part numbers and they were different for the air box sub assembly that attaches to the actual carbs. So this leads to 2 questions: 1. Do the F2 and F3 have different carbs? The holes don't match up from the air box and the carbs. 2. Air filter is the same but I just can't seem to get it to fit right, so is there a trick or is it just a cram it in there until it fits? This just doesn't seem right to me. In my head it should just slip into place and it doesn't. Neither one of them. Attached is the original air box sub assembly that I got with the bike. Seems to be off a late model F3 as best as I can tell.
Chime in and let me know whats what.

They have different carbs & different air box. Your cables look properly routed to me. Make sure your grip is not squeezed against the throttle tube housing, that would cause some sticking. A little lube in there might help. My air filter seems a little on the big side, its a K & N and if I put the front & rear in its grove it bulges up in the middle a little until I squeeze it all together with the lid on. You can unhook the choke and move it by hand to see if it is sticky at the carb or its the cable/mechanism.