Suppose the Corp player has a paid ability like Corporate Troubleshooter that interacts with Ice. The runner has a breaker they want to use to break that Ice, the Corp wants to use Troubleshooter to make it bigger. How does the timing work?

A) The Corp must use Troubleshooter during a 'paid ability' window before the Runner activates any icebreaker powers. (During step 3.1)

B) Icebreakers are Paid abilities, so the Corp can wait until the runner buffs his Icebreaker during Step 3.1, then interrupt him before any Break subroutines are used to use Troubleshooter, to force the Runner to futher buff his icebreaker

C) Icebreakers are Paid abilities, and the Runner has priority, so the Runner can activate any number of paid abilities (including buffing icebreakers and breaking subroutines), so the Corp must activate Troubleshooter as a paid ability earlier in the timing structure, probably during step 2.3 Rez Ice.

I assume this would apply the same to Project Wotan, but not Tyr's Hand, because Hand is a prevention effect.

© is correct. When the runner approaches the ice, he has the opportunity to trigger paid abilities, as many as he likes, before the ice is rezzed (if he suspects or knows about a Tollbooth, he can dump credits into a useless icebreaker at this point).

Then after the runner passes, the corp has the chance to rez cards and use paid abilities: specifically, to rez the Ice, Rez the Corporate Troubleshooter, and trigger the Troubleshooter's ability. You'd want to

Then you move on to step 3, and the runner encounters the ice, at its new strength.

Tyr's Hand is a weird one, whose wording enables it to rez and activate in step 3.

B) Icebreakers are Paid abilities, so the Corp can wait until the runner buffs his Icebreaker during Step 3.1, then interrupt him before any Break subroutines are used to use Troubleshooter, to force the Runner to futher buff his icebreaker

Nope - check the rules again. ONLY Prevent or Avoid effects can be used an interrupts. Troubleshooter is neither. If the runner is at step 3.1, they have priority for paid abilities (as it's their turn) and so can boost AND break before you do anything.

The best time to troubleshoot your ICE is step 2.1 or step 3.0 (but note that Troubleshooter must be rezzed no later than step 2.1 regardless, or you miss your chance).

© is correct. When the runner approaches the ice, he has the opportunity to trigger paid abilities, as many as he likes, before the ice is rezzed (if he suspects or knows about a Tollbooth, he can dump credits into a useless icebreaker at this point).

Then after the runner passes, the corp has the chance to rez cards and use paid abilities: specifically, to rez the Ice, Rez the Corporate Troubleshooter, and trigger the Troubleshooter's ability. You'd want to

Then you move on to step 3, and the runner encounters the ice, at its new strength.

Tyr's Hand is a weird one, whose wording enables it to rez and activate in step 3.

Actually Tyr's Hand still takes effect at 3.1; it's a prevention effect and so interrupts the normal priority order. Like Zaibatsu Loyalty the wording allows your to rez after the runner has declared for effects and paid costs, but before resolution.

I didn't have the timing charts handy, so I just said "in step 3." I'm sure you're right that specifically, it's in step 3.1.

© is correct. When the runner approaches the ice, he has the opportunity to trigger paid abilities, as many as he likes, before the ice is rezzed (if he suspects or knows about a Tollbooth, he can dump credits into a useless icebreaker at this point).

Then after the runner passes, the corp has the chance to rez cards and use paid abilities: specifically, to rez the Ice, Rez the Corporate Troubleshooter, and trigger the Troubleshooter's ability. You'd want to

Then you move on to step 3, and the runner encounters the ice, at its new strength.

Tyr's Hand is a weird one, whose wording enables it to rez and activate in step 3.

Correct.

I have a question on how Tyr's Hand works.

So I had the Tyr's Hand upgrade installed on my Head Quarters and my Opponent decided to make a run on HQ. He matched strength with my ice by paying X credits, then he declared to break the first subroutine at which point I rez'd Tyr's hand to prevent breaking of that subroutine as I wanted him to take the effects of that specific subroutine.

Tyr's hand Prevents, does that mean, his attempt was prevented, aka not allowed, before he spent whatever he is using to break it, or he spends credits or clicks, to break, and is prevented after the expense?

After.

Be aware though that the runner can simply break the subroutine again, provided he has the resources (credits, clicks) to do so. Unbroken subroutines only resolve in step 3.2 after the runner passes on doing any further paid abilities in step 3.1.

Be aware though that the runner can simply break the subroutine again, provided he has the resources (credits, clicks) to do so. Unbroken subroutines only resolve in step 3.2 after the runner passes on doing any further paid abilities in step 3.1.

Correct. Tyr's hand is usually used when the Runner spends their last Credit breaking subroutines or when they use another resource (such as Clicking through a Bioroid) or Deus X to break it.