Can a tantalum capacitor be used in a high energy circuit?

Warning: NEVER use tantalum capacitors in a "high energy" circuit where voltage can EVER exceed the voltage rating of the capacitor. Even the shortest spike (sub microsecond) can puncture the oxide layer and "away it goes". Almost as much fun as a LiIon battery!. Related: electronics.stackexchange.com/questions/9120/

What is a tolerance for a tantalum capacitor?

A factor of 2 in value is unlikely to be relevant. Capacitors in some cases can have tolerances of +100% / -50% (wet aluminium electrolytic) but may be +/-5% or 10% or 20% for Tantalum. Warning: NEVER use tantalum capacitors in a "high energy" circuit where voltage can EVER exceed the voltage rating of the capacitor.

Is it safe to use ceramic capacitors instead of tantalum?

Also, if one use ceramic instead of tantalum, it's generally safe use lower value (like 10uF), but one need to check datasheet. True, but soldering those huge-value ceramic capacitors is a problematic operation.

Why do tantalum caps fail?

As we're aleready talking about derating and fried tantalum caps: Besides (even very short) voltage spikes causing tantalum caps to fail catastrophically, they are also very sensitive to current spikes (as they will appear when you hot-plug the power connector into the drive).

Can a capacitor be used to recover data from a hard drive?

If you just need the drive to recover the data, any half-decent electrolytic (including tantalum) capacitor will likely do the job long enough until you finally scrap the drive. Don't worry too much about the ESR. As the cap appears to be just in parallel to the 12 V input, it's not worth counting every milliohm.

What is the minimum capacitance a capacitor can use?

I would guess that 22μF 22 μ F is the minimum capacitance that the application can use. Part characteristics can differ as their voltage rating increases, so be careful not to go 'too' high. (Don't put a 100V capacitor where there once was a 16V part).