Tenant Request leave early in initial Fixed 6months AST

Tenant wants to leave and end current 6mth ~AST at month 5.
They have written to state the above ( giving the required 2 months notice correctly), but also stating that they will stop paying rent, hand the keys back and have meters read for elec / water and advise Council and stop paying these from Month 5.
I am happy in principle to assist as long as I am not out of pocket nor cause some legal issue by trying to help out.

(1) Can I say , I will readvertise and if I find a suitable tenant I will release them from their 6mth AST contract early , but only if & when the new contract with the new tenant is signed, and until such date the (existing) tenant will still be liable for full rent, (and all Utilities etc)., as I have no idea as to how long it may take?
(2) Should I include, or even am I allowed to claim any costs ( such as for readvertising).
(3) Are there any other points I should consider?

Yes you can say you won’t release early unless you fill it, you can also say you won’t release them at all, but then they are within their rights to be awkward and keep the keys, whoever has possession is responsible for the council tax and energy bills.

You can’t include costs for readvertising, but you can refuse to release them from the six months. I’d prob say to them if they give back the keys you will see if you can fill it and either come to an arrangement with them now or have your next tenants start date be just after their official end. If they are gone and you have no wear and tear you would maybe be better off that way

Legally, you are entitled to the full six months’ rent. They can’t just decide to leave the tenancy early. But it’s only one month, and if they feel you treat them unfairly and they retaliate, it will harm you much more than one month’s rent. I would try to come to a compromise with them.

(1) is reasonable, I would do that.
(2) Potentially risky from a legal point of view and could get you in trouble, but I’m not a lawyer. If you feel like you want to charge them something (which is understandable), suggest as a compromise that they’ll pay x% of the last month’s rent and choose x such that it covers your advertisement costs. But I wouldn’t tell them that they have to pay for advertising.
(3) No idea.