Resolved: Instead of giving ITIL role to snc_internal users (as this will have a financial impact), therefore I resolved the issue with ACLs.

Got the solution with the below link:
Solved: How to allow users on watch list to post additiona... - Page 3 - ServiceNow Community

Just add snc_internal role to all my 4 custom ACLs and remaining was the same from above link.
First you need to give Read access and then Write access at table level and Field level. (Screenshot attached below)

1) table.None (Read operation) - Just added snc_internal role and no conditions.
2) table.None (Write operation) - Just added snc_internal role and 1 watchlist and 2 state field conditions.

3) table.Additonal comments (Read operation) - Just added snc_internal role and 1 watchlist field condition.
4) table.Additonal comments (Write operation) - Just added snc_internal role and 1 watchlist field condition.