Please see my answers below:
Since I have the option to let users get a paid membership (choose a listing package),
does it make some sort of membership level, so it’s possible
to hide/show information on the site, based on membership level?
–> Hide/show info is not a feature developed. Membership is strictly for submission property (number of properties user can submit and number of properties user can make as featured)
Example: If I make a custom field, would it be possible to hide that field on the
frontend for all others than users with a certain membership(s)?
If a certain membership, they are able to see the contact information of a property
before a booking is made, even when it’s chosen to hide it for regular users
—> This must be reviewed as custom work and it’s intensive development. If you wish us to give some directions on possible costs, please open a custom development ticket here http://support.wpestate.org/