99 Isuzu Rodeo please help!

99 isuzu rodeo 2wd. My question has two parts to it. One is that my fan (radiator or fan that blows a/c i don't which one really) keeps blowing after my engine has been shut off. It will blow for about 15 seconds or so. However, it usually stays on when i have my air condition (or just air) blowing. So usually to fix the problem, before i turn off the ignition, i shut off the air and it doesn't do it. But in the morning, regardless if i turn the air off, it still does it.
The second thing is also in the morning when i first turn on the rodeo, the RPMS stay high while changing the gears (it's a standard), this happens for about a good 5-10 minutes i guess while the engine warms up, then i can change gears and they stay where they're supposed to be.
I just wanted to know if anyone can help me out or give me ideas as to what the problem might be before i take it into a mechanic. Thanks a lot.