GTM verify server availability - appreciate more indepth details on the process

1/ how does the GTM check the availability of the server?

GTM includes three methods of determining resource availability:
 1. Limit settings
 2. Monitor availability requirements
 3. Virtual server dependencies

Does it just refer to info locally on the Gtm, or info from the bigip, or Derform a complete check all the way to the actual server.

iQuery and big3d agent run locally on GTM but these agent collect all the information from respective LTM(bigip).LTM response back to GTM.

2/ will it override a health monitor that has't failed (ie almost like an inband monitor)

 Monitor works based on configuration.