I will use Crypsis - but assume I am asking for generic timing rules.

Can I announce a run, wait to see if they rez the ice, then take an action to put a virus counter on Crypsis?

Can I play an event card during a run?

Basically - are there "top level" actions...or is everything able to respond?

Another one - can you activate a "prevent 1 net damage" action after the corp player does something that will cause me to take 1 net damage?

Any time you spend a Click to perform an Action on the list of Actions on pp. 12-15 of the Rulebook, it is an Action. All Actions are top level Actions. You cannot play an Event during a Run. You cannot load Crypsis during a Run. You cannot install a Card during a Run.

Other powers that use "thing: effect" are called Paid Abilities. You spend "thing" to cause "effect" to occur. Whenever there is a Paid Ability window (a green arrow in the timing chart), the acting player gets to use as many Paid Abilities as they want, then their opponent gets to use as many Paid Abilities as they want, then you continue taking turns as long as both players continue to use Paid Abilities.

"Prevent" and "Avoid" effects ignore the normal timing rules and can be used to interrupt the thing they Prevent or Avoid.

I will use Crypsis - but assume I am asking for generic timing rules.

1) Can I announce a run, wait to see if they rez the ice, then take an action to put a virus counter on Crypsis?

2) Can I play an event card during a run?

Basically - are there "top level" actions...or is everything able to respond?

3) Another one - can you activate a "prevent 1 net damage" action after the corp player does something that will cause me to take 1 net damage?

There is a detailed timing chart in the core rulebook that is expanded with minor corrections in the FAQ that will answer most questions.

1 and 2, no, both of those require you to spend clicks, which, all things being equal, you cannot do during a run. As said above, you have to play out the current action before you take subsequent actions.

3--Core set rules, p 21:

Prevent or Avoid

Some card abilities use the words “prevent” or “avoid.” Prevent

or avoid effects are the only effects which can disrupt another

effect. A prevent or avoid effect states what it is preventing

or avoiding, and an effect that is prevented or avoided is not

resolved. Prevent or avoid effects can be triggered whenever the

effect they are preventing or avoiding is resolving.

thanks guys - looking forward to getting into this deeper.