Tags can be filtered as described in the H2o documentation.
Unfortunately, the "date" filter for H2o only allows for you to format the date according to php's date function, which does not do timezone conversion.
e.g.
{ticket.date_added | date "M d, Y H:i:s A"} is "Feb 09, 2016 23:17:42 PM" UTC
The timezone conversion is an additional step, so either a new tag would need to exist that displays the date in the appropriate timezone, or better yet, H2o would need to be extended to support a new filter for performing the timezone conversion.
Only the tags shown on the Support Manager page documentation would be available. It's possible that a client may not be assigned to the ticket at all, if the ticket were emailed in, for instance. The plugin doesn't make additional queries to allow for these tags due to the performance hit it would incur. however, that may be a good feature request. The client, the contact that replied, the staff, and the department might be a good set of additional tags.
The {ticket.code} is not necessarily a unique code, and it could be guessed. The {ticket_hash_code} does change per email, is unlikely to be guessed, and is used to determine the ticket the email is associated with.