Basic battery query--Inspiron 2200

I'm still new to notebooks. I have a new Inspiron 2200 with the Lithium ion
battery.

Now, I've read that it is a good idea not to charge the battery when it is
very hot, so:

1) First scenario, I'm working happily away when all of a sudden I get the
low battery warning/switch to AC power. I don't want to close anything down
as say I am in the latter stages of an online poker tourney. So, I just plug
in the AC adapter, although at this point the battery is quite hot. Am I
doing any damage?? Should I remove the battery after plugging in the AC?
(Would that even work).

2) If I have a choice, am I just better off running my laptop on AC?? Again,
should I/canI remove the battery in such a case.

3) OK, using battery and it is getting low. I shut down the computer. Since
the battery is still very hot, should I wait about 30 minutes before
starting the charge routine (all with computer off)

Mel