GTM Qs - Synch group / wide IP / licensing ...

Q1. GTM and LTM synchronisation are entirely unrelated and synchronise different objects. Most GTM objects are synchronised via gtm sync, but a notable exception to this is GTM listeners, since they are actually LTM virtual servers, are are unique to each individual GTM in any case (it wouldn't make sense to synchronise the listeners across the gtm sync group)

Q2. You can add an iRule to a listener - it will be an LTM irule, which means it receives LTM events, as opposed to a wideip with an iRule which will receive GTM events, and is limited to commands that make sense to GTM.

Q3. The GTM license enables certain LTM features behind the scenes in order to function properly. Different versions of BigIP act slightly differently in what you see in the GUI. If you have a GTM-only license, you'll be quite limited (and won't be able to add irules to listeners, for example)

Q4. DNS services (DNS Express, DNS cachine) is actually part of the LTM license, not GTM, though it works with the GTM product via options turned on in the the GTM listener's DNS profile