‘Is this available yet?’ is more natural and this does not depend on whether you are using British English or American English.
Adverbial position is something that one learns from experience. Some adverbs are more natural-sounding when placed before an adjective; others are best placed after it. In your case ‘Is this already available?’ sounds better, but I cannot think of a grammatical reason as to why.
Note that there is a subtle difference in meaning between the two phrases. ‘Is this available yet?’ is more expectant, whereas ‘Is this already available?’ is softer and more polite, at least to my ears.