Noise at the kitchen faucet

i replaced the diverter valve in my delta kitchen faucet. now the two handle hot and cold water makes a loud noise when turned on. i can almost stop the noise with some tinkering with the temp mixture. i know there is a way to fix this with out replacing the whole thing. any sugestions? while we're in the kitchen sink... there is no trap directly under the sink ( it's in the crawlspace/ basement ) when the water starts to go down the drain, it gurggles, bubbles and just takes way too long to go away. my question is can i cut the pipe and put some kind of trap in? my thinking is the gurgling is caused by the water rushing to escape the long pipe down an the air gets trapped in the line. causing the delay back up. the water does go down, rather quickly. but when pouring very hot used pasta water into a strainer, holding the pan and strainer at the same time while pouring "ain't working for me."
thanks for your input.

drain

About the only thing that could make that sound would be the diverter, so you may have a bad one. I don't know who installed your sink drain, but it was not a plumber. A vent under the sink would do absolutely nothing to keep the trap from gurglne. At least part of your drainage problem could be air trapped between the sink and the trap, and if so, an AAV vert would not help that anyway. You may have a partially plugged drain line which could also cause your symptoms.

drain

thanks. i know that there is air trapped. i went under the sink and here's what i found... from the drain on the sink it's connected to a brass pipe (6" or so) that is connected to an elbow. then 6" to 8 " horizontal plastic pipe (the white pipe ) then another elbow, to a vertical pipe that goes through the cabinet and floor to the crawlspace/ basement to the trap. what i want to know is would it be effective to put a trap directly under the sink to stop the trapped air from gurgling?

Sounds all wrong, from your description it sounds like an S trap, but then you say it goes down to the trap in the basement? This would never drain properly, do you have a vent?

i went into the crawl space/ basement... looked at the trap. there seems to be a vent pipe attached after the trap. and i noticed the trap is without a nut on the bottom as to check for a clogged line, and or other debris.

Sounds to me that it is a mess and really needs a total replumbing. Otherwise you're chasing ghosts.