I want to find nodes/pools which are associated with all pool/VIPs?

Well in CLI its pretty easy with one-line command, to lookup an VIP or to look up a pool, one-line is a favorite. Try it.

To find a node if its part of any pool. where 1.1.1.1 is the node that you want to check if its part of any pool.

tmsh list ltm pool one-line | grep 1.1.1.1 | awk '{print $3}'

The output will be just the pool names.

Similarly to find the pools referenced in any VS. where my-app-pool-name is the pool name

tmsh list ltm virtual one-line | grep my-app-pool-name  | awk '{print $3}'

The output will be just the VS names.

Same you can use to find the VS setup with a VIP, where 1.2.3.4:443 is my VIP

tmsh list ltm virtual  one-line | grep 1.2.3.4:443  | awk '{print $3}'

If you want to do it on bulk, you can simply put a bash script and put a loop to find both the pool names and the corresponding VS details.