Learn Turkish: Sunucu maksimum kapasitede olabildiğince hızlı çalışıyor. - The server is working as fast as possible at maximum capacity.

It breaks down into ol- (to be) + -abil (ability) + -diğ (participle) + -i (3rd person possessive) + -nce (equative suffix). Together, olabildiğince literally means 'as much as it can be', which translates perfectly to 'as [fast] as possible' when paired with an adjective or adverb.

Could we use kadar instead of the -nce suffix here?

Yes! You can absolutely say olabildiği kadar hızlı çalışıyor. The forms -diğince and -diği kadar are generally interchangeable when expressing 'as much as possible', though olabildiğince has become a very common set phrase.

Why use olabildiğince instead of attaching the pattern directly to the main verb, like çalışabildiğince?

When you want to say 'as [adjective/adverb] as possible', you use olabildiğince (or olabildiği kadar) right before the adjective or adverb. If you said çalışabildiğince hızlı, it would sound strange, roughly meaning 'fast, as much as it can work'. You would only attach the pattern to the main verb if you dropped the adverb entirely, like çalışabildiğince çalışıyor (It is working as much as it can).

I've seen sunucu used for a TV presenter. Does it mean a computer server here?