Machine learning CAN also be used as a modifier (LIKE an adjective). Example:
The company developed new technology like machine-learning computer vision.
I'd use hyphenation in machine-learning here because it's modifying something else, and particularly because there are multiple modifiers.
To say that something turns out to be the case, you can use 'prove' followed by either: an adjective, or an infinitive verb and an adjective or noun.
The tools proved useful.
The new employee proved to be a fool.
The car proved to have a flat tyre.
Of your sentences, only the first is grammatical. The second uses the wrong verb form after 'proved' (must be ...
1 - The correct choice here is getting. Get does not really make sense in that sentence. If you are using 'in regards to' followed by a verb, use the -ing form.
2 - working is also the right choice here for saying she has become employed somewhere. If you use 'to work' it sounds like you are saying that she was already employed there but only recently doing ...