There is very limited functionality on IME that is supported for IOS IPS. You won't be able to update the configuration/signature via IME for IOS IPS.
Here is the list of what is supported on IME for IOS IPS for your reference:
http://www.cisco.com/en/US/prod/collateral/vpndevc/ps5729/ps5715/ps9610/data_sheet_c78-459033.html
IME is more suitable for IPS appliance, or IPS hardware module.
To answer your question:
1. No, it won't make any changes to the router config. It doesn't even support the IPS configuration changes.
2. To enable HTTPS on the router: ip http server
At the moment, your config has "ip http access-class 23" however, i can't see any ACL 23. To restrict access only from a few subnets/hosts, you can configure ACL and apply it to "ip http access-class" command. Otherwise, if you don't need to restrict from specific subnets/hosts, just remove the above command.
3. It will use self signed certificate on the router.
Hope this helps.