Learn Italian: Questa nuova tendenza cresce rapidamente.

You would add sempre più before the adverb. The sentence becomes Questa nuova tendenza cresce sempre più rapidamente. While sempre più literally translates to 'always more', it is the standard way to express 'more and more' or progressive degree in Italian.

How exactly is the adverb rapidamente formed here?

The suffix -mente is the Italian equivalent of the English '-ly'. To create an adverb this way, you take the feminine singular form of the adjective (in this case, rapida) and attach -mente to the end.

Does the adjective nuova have to go before the noun tendenza?

Not strictly, but it is the most natural word order for this sentence. Common adjectives describing age, size, or beauty usually precede the noun. If you wrote Questa tendenza nuova, it would put much stronger emphasis on the word 'new', as if you were directly comparing it to an old trend.

Can cresce also translate to 'is growing' instead of just 'grows'?

Yes! The Italian simple present tense covers both 'grows' and 'is growing'. While you could use the continuous form sta crescendo to emphasize that the action is happening exactly at this moment, using the simple present cresce is completely natural for describing an ongoing, general trend.