04 Tacoma Error Codes P0441 & P0446

Background: a few months ago, I had my truck in for service; they checked my air filter and said it was dirty but they didn't have a suitable one in stock. No big deal; I bought a replacement at a parts store with the intention of replacing the old one when I got home, but every time I started or turned off the engine, I would hear a thump coming from the front right side. Finally took a look under the hood in a store parking lot and saw that they had left the air filter housing wide open and devoid of any filter. I put the new filter in, closed up the compartment and went on my merry way...

When I filled my gas tank last week, the pump kept shutting off as though it was full; I had to run it at a trickle to fill the tank. Then, this past Thursday night I started the engine to leave work and my check engine light was on steadily. I stopped at the parts store Friday night to have the codes read; they came up as P0441 and P0446. I've been scanning forums to get some insight, and have checked the hoses and found none that appear cracked. However, I noticed that the hose that should be connected to the side of the air filter housing was wedged between the housing sections. I connected it to the port coming off the housing. When I started the engine, the Check Engine light was still on, but I've seen mention of a "drive cycle" that has to happen before the diagnostic system will retest and reset the light; how long does that generally take, or is there something I can do to force it to happen? Does this sound like it would have caused the error codes, or am I likely to have to do some more detective work?