The text says

Re-attempt: Whether or not the task may be re-attempted, and recommendations on penalties for failure

Does that mean that any failure information in that block applies only to re-attempts, or does it apply to the initial attempt?For example, if you fail a Climb test, do you fall, or only fall if you try again?

It applies to all attempts.

The re-attempt part of the Skills is basically the consquences for failure. What happens if you fail and if you can try again.

Note that if you fail a climb test you only fall if you fail by more degrees than you Strength Bonus.

So for climbing if you fail your climb test badly you can reattempt the climb after you have fallen.

Penalties for failure always apply - one of the penalties can be not being allowed to try again.

Rerolls aren't the same as re-attempts.

Take a tech-use test in two situations:

if I fail a tech-use test to disarm a 'normal' lock, the door remains locked. If I reroll with a fate point and still fail, it remains locked. Nothing stops me trying again, but I will now have spent twice or more the normal time span trying to pick it.

If I fail a tech-use test to disarm a door with some sort of security system, it deadlocks itself. If I reroll with a fate point and still fail, it remains locked and now the control panel is shut out. I cannot try again and we have to find another way in.

What about just adding another section to the "Skill Blocks" that says

Re-Try: (can it be retried)

Failure: (consequences if failed)

if I fail a tech-use test to disarm a 'normal' lock, the door remains locked. If I reroll with a fate point and still fail, it remains locked. Nothing stops me trying again, but I will now have spent twice or more the normal time span trying to pick it.

If I fail a tech-use test to disarm a door with some sort of security system, it deadlocks itself. If I reroll with a fate point and still fail, it remains locked and now the control panel is shut out. I cannot try again and we have to find another way in.

This isn't how Fate re-rolls work. They effectively replace the original result, they're not re-attempts. If you fail, then spend a Fate to re-roll and still fail, you've only made one attempt. If you shoot a gun and miss, then use a Fate point to re-roll, you don't end up using twice the ammunition.

Correct. Note that I said if you reroll and fail you can still try again. It's trying again that means you'll have spent twice as much time.