eviction of tennants

Tenancy Types and Management

On 1st February we issued a Section 21. The property had sustained damage and also furniture was damaged.
We have now (1st March) reached a position where no rent has been paid for 10 weeks, therefore we are going to issue a Section 8, is this correct?
If during the 16 days they remedy any one of the above breeches are we still able to go ahead with the N5 and N119 proceedures or do we have to start again. We think it likely they might pay some of the rent under the assumption that this will halt proceedings but they will not do anything about the damage done.
We would of course just like to get them out and would like your advise.
Thank you