Wizkids Rules!

Varel states that she must "Discard to cancel one attack..."

Does she automatically cancel the first attack against a ship she is on?
or
Can the player choose which attack to disable against the ship she is on?

16. If one of my own cards requires me to "discard" or "disable" the card in order to activate its special ability, can I choose when to use this card (e.g. Worf (Starter), Uhura, McCoy)?
Yes.

As the FAQ states when you discard or disable a card to do it's ability it is optional.

You can discard Varel to cancel any one attack and you are not forced to discard her to cancel the first attack.

If I am required to "Discard" or "disable" a card to trigger its ability does the ability still trigger if I use a card to keep Varel from discarding.

Weyoun: Disable Weyoun to prevent 1 of your [CREW] from being disabled or discarded this round.

Yes, you may use Weyoun to stop Varel from being discarded after Varel has been used to cancel an attack.

If you prevent Varel from being discarded (Weyoun/Crusher) can you use her again to cancel another attack?

No, you would only be able to use Varel 1 time per round.

Optional Text Once Per Turn

All cards that contain non-ACTION text abilities that are optionally triggered by a player, may only be used once per round per ship per card.
Example 1: If you use Geordi La Forge to force an opposing ship to reroll 1 defense die you may not use it a second time in that round
Example 2: You may discard Varel to cancel an attack. If you stopped her from being discarded you may not use her text again in the same round.
Example 3: You may use Li Nalas to stop your Captain from being disabled. But, if he is reenabled during the same turn, you may not use his game text again that round.

Does this mean that Weyoun may only be disabled once per turn as well?

Weyoun is optionally disabled by the player. Therefore he could only use his ability once per turn.

He could be disabled repeatedly (if somehow undisabled between each action) through other cards game text, but not his own.

What about Mr. Spock ("You may convert all your [Battlestations] results into [Hit] results") or Breen Aide ("You may convert 1 blank result into 1 [Hit] result")?

Both of these cards contain the word "may" so they are optional to use. They may only be used once per round.