Does Electrum provides any API? Does Electrum provides any API? If yes, please let me know if there's any dedicated documentation available.

Also, does Electrum support Bitcoin Cash?

Purpose:
I want to integrate Electrum into my application for wallet service and seeding capabilities. I'm planning to run full node for BCH and BTC.
Yes for sure, You can send requests to electrum servers or your server (recommended) by sending JSON-RPC requests. 

Take a look on Electrum documentation 

https://electrumx.readthedocs.io/en/latest/protocol-methods.html

for bitcoin cash use Electroncash  same commands work.

For example, to broadcast a hex transaction you can call

{"id": 1, "method": "blockchain.transaction.broadcast", "params": ["YOUR_HEX_TRANSACTION"]}

There are no wallet commands available, but blockchain commands.