dead said:
1) When an invisible creature is moving, do you use a Spot check or a Listen check (or both!) to know it's there?
Either or both.
Look up Invisibility in the Special Abilities and Conditions section of the DMG, or in
this document.
2) When you are in melee with an invisible creature, do you have to make a Spot check before you can attempt to strike it?
You don't have to, but it can help.
There is a difference between knowing there is an invisible creature nearby (base Spot DC 20 for a creature who is not actively trying to be still), and knowing which square it is in (which adds 20 to the Spot DC).
So with a DC 40 Spot check, you know which square the invisible creature is in. (This is the meaning of the term 'pinpoint'.)
If you have an invisible creature pinpointed, you can attack it, with a 50% miss chance.
If you don't, you can still attack it with a 50% miss chance... but you also need to state which square you are attacking into. If you guess the wrong square, you will miss no matter what your attack roll and miss chance roll say.
There are other ways of pinpointing an invisible creature (for example, if he makes a melee attack from an adjacent square and hits, you know which square he attacked from... although he might move before your turn comes up), but with a Spot check, it's generally DC 40.
Most of this is in the document linked above.
-Hyp.