It's interesting to see that the verb to go is also used to talk about the future in Welsh. I'm always surprised by how many languages have this construct which I would expect to be more idiomatic.
Aros is a verb here, right? So, i can say "dw i'n aros" to mean "I stay"?
Correct. Aros is a verb-noun meaning 'staying/to stay' and also 'waiting/to wait'
Dw i'n aros mewn gwesty - 'I am staying in a hotel' '
Dw i'n aros am Sioned - 'I am waiting for Sioned'
can aros mean stop too?
It can. As in heb aros - without stopping/waiting, or
Where I come from in Wales we often say"Are you going to stop?" in the sense"are you going to stay" eg Stop and have a cup of tea = Stay and have a cup of tea."
Is this construct with 'mynd' something Welsh has natively had, or is it due to English influence?
Or did English get it from Welsh?
I even think that French is influenced by Welsh. Many words in French are different from what you might expect.
In stead of octo, otte or ocho, they say huit. Wyth? Aujourd'hui... Heddiw?
May be coincidence, but it is interesting.
It is a pattern used in several languages.