Tlhokaina For example, could one profile be running apps (in the background) using VPN whilst another profile is accessing the internet but isn't using VPN?
Yes
Tlhokaina Or one profile is connected to one AP whilst at the same time another profile is connected to a different AP?
No. To my knowledge/experience user profiles inherit the AP of the Owner profile and vice versa (if you change it on the user profile, it also changes the AP on the Owner profile).
Edit: Guest profiles do not have permission to change the AP at all