I have an modern ali hardtail frame that is designed for forks up to 551mm axle to crown length. Will I risk ripping the head tube off if I fit a fork with an axle to crown of 566mm?

Probably not, but you can’t be certain.

No.  tiny % change of around 2%.

As long as you ride the same trails in the same manner, it won’t make any difference. It’s about a 3% increase. The problem with fitting longer forks is that they usually have more travel, which encourages you to ride more aggressively. If you take a lightweight XC frame and fit burly 150 mm travel forks then thrash it on rough DH courses, it will break because it’s not designed for that sort of riding.

Just don’t be honest in the warranty claim 😀, I constantly up travel by 10mm, even 20mm on one occasion, but as above it barely increases the chance. If it was that easy we would all be a few percent away from ripping our headtubes off.
I think Blake on GMBN runs a 170mm lyrik on his Nukeproof Scout.

Ifyou’re of average weight or below (for an adult male) then there is loads of capacity left.

No