Can we have negative conditions in Correlation filters or we can only use SQL Filters to have -ve conditions on User/System Properties?
Correlation filters check for equality and equality only. If filter criteria are not satisfied, the message is ignored. You can use SQL filters for more sophisticated rules. You can find more details here.
Is it okay to delete and add a new rule as we have the requirement to update the filters (It's Always to add an extra condition in the sql filter) based on a trigger that might happen at any point of time?
You cannot modify an existing rule, only replace. Rules can be added, deleted, or replaced at any point in time. Just keep in mind that when you do so, what kind of impact it can have on the system. If you remove the existing rule while a message is arriving and the new rule has not been added just yet, the message will not be received by the subscription that is affected and the message will be lost.