Are they used by older people/in formal situations?
This depends on the word. Some are old enough and safe in business settings (e.g., メモる, トラブる, サボる). Some are rare and/or slangy. They are generally avoided in very formal legal documents, etc.
Are they really slang?
Generally yes, but many are widely used in day-to-day business settings, and there are many that are considered as industry-specific jargon shared by experts. See this for examples.
I'm curious if youth invent them or anyone starts using them.
Young people tend to like coining new words, and I suppose this is true in any language. There is nothing special in relation to loanword-based godan-verbs.
Are 造語 made because there is no "traditional" Japanese word for them?
Sometimes yes (of course there was no traditional Japanese version of グーグル), but usually no. The main reason is because such 造語 sound catchy, shorter, humorous, etc.
Or can any loanword be made into one?
Three- or four-mora loanwords ending with ル are most easily turned into godan verbs. Longer loanwords may be truncated and turned into godan verbs, but it's less common. See this.
Do you use both stem + る and loanword + する or do you have to choose one? Like I've heard of ゲットる and ゲットする, is one used more/differently?
They are hardly interchangeable. Loanword + する is the standard way to use loanwords as verbs. Besides, not all loanwords take する in the first place. For example, you have to say グーグルを使う, not グーグルする. By the way, ゲットる should be very rare (I haven't heard it).
