Do parents have their own individual chat channel in Maud once admitted?

Yes, there are two types of chat channels, group and 1:1 channels.

For example:

To chat with all proxy supports, you will either need to use Supports + Provider Team or Supports + Therapist
To chat with an individual parent, you can chat in Proxy Support 1 + Dietitian or Proxy Support 2 + Dietitian

For more information on what chat channels are available, refer to this article