Yeah, people often confuse the past and future endings with the plural pronouns ni, chi and nhw as it's only one vowel difference:
Arhoson ni "We stayed" | Arhoswn ni "We'll stay"
Arhosoch chi "You stayed" | Arhoswch chi "You''ll stay"
Arhoson nhw "They stayed" | Arhosan nhw "They'll stay"
If it helps, the past tense ones all have o as the vowel, and -on rhymes with "gone" as in "been and gone".
The future tense vowels in order are "w-w-a" i.e. "ooh-ooh-ah", which sounds like a monkey. It helps some people remember!
Yn is used with definite nouns:
Arhosan nhw yn yr ysgol "They'll wait in/at (the) school"
Mewn is used with indefinite nouns:
Arhosan nhw mewn ysgol "They'll wait in/at a school"
If you want to be clear that they're "inside", then you can use (y) tu mewn i. This can be used with definite or indefinite nouns.
Arhosan nhw tu mewn i'r ysgol "They'll wait inside the school"
Arhosan nhw tu mewn i ysgol "They'll wait inside a school"
This is explained in the course notes somewhere. Welsh uses the definite article yr/y/'r in front of places that we habitually go to one of - bed, church/chapel, work, pub, shop, town, etc etc. English uses 'the' for some of those but not for others.
Does this just mean physically staying/waiting at school, or can this "staying in school" also have the meaning of "continuing to study"? Thank you.
Usually waiting/staying. For continuing to do something you would probably use parhau or aros ymlaen.
Have a look in the on-line Geiriadur yr Academi for examples which best fit your intended English meaning.