Learn Finnish: Hurahdin täysin tähän uuteen harrastukseen. - I got completely hooked on this new hobby.

The verb hurahtaa (to get hooked on, to fall for) is a verb of reacting and committing. Just like keskittyä (to focus on) or suhtautua (to react/relate to), it requires the thing you are reacting to or focusing on to be in the illative (the "into") case. In Finnish, you get hooked "into" a hobby.

Is the verb hurahtaa formal or informal, and what is its exact nuance here?

It is a colloquial, highly descriptive verb. While it can literally mean a quick, swooshing movement, here it is used metaphorically to mean suddenly becoming wildly enthusiastic or obsessed with something. It is very similar to saying you "went crazy for" a new fad or "fell down the rabbit hole" in English.

I always forget how to decline words like uusi. Why is its illative form uuteen?

Adjectives and nouns ending in -si (like uusi, vuosi, vesi) usually have a stem where the -si changes to -te- before adding case endings. This makes the stem uute-. When we add the illative ending -en, we get uuteen.

Why does the ending of harrastus change to -ukseen in this sentence?