UK Question about landlords and tenants?

Showerheads are part of the fixtures and fittings, so no
It is as simple as getting a new showerhead
Sorry

Try decalcifying the shower head...this is a common problem.

You have an Assured shortHOLD tenancy and no you can't withhold rent, that would be illegal......... before you start doing anything you need to CLEAN the shower head and make sure it is not dirt built up inside or hard water that has calcified which needs cleaning off as even if the landlord sends someone to 'fix it' if that is the reason you will be charged for the maintenance. You write a letter/email and keep a copy on it note the request date you first asked for maintenance, after a week if you do not hear back then contact the council housing department and ask to speak to the private housing officer who can advise you ( often they will contact the landlord and 'request' they respond by x date)

Consult a lawyer. 1) You need to have "properly" reported the issue and reminded them 2) Laws vary. Whether you can have it done and deduct the cost will depend on where you live. Such laws are not country-wide.

Report it to them IN WRITING, and request a resolution within 1 week.

If it's not in writing, it's not official.

that is very true but this is not life threatening nor making the place uninhabitable

1) always contact a landlord regarding all disputes via e-mail or letter (date and keep a copy) NEVER just phone
In your case I would do this weekly (then he cant claim he forgot, or thought it was fixed)

2) consult citizens advice taking a copies of the emails/letter(s) and any response - most likely they will put you onto environmental health

3) if you have the cash - consult a solicitor (get a receipt for the cost- cos you may be able to sue the landlord)
(you may not need to do this - citizens advice might handle the case)

My advice
When renting ALWAYS take out renters insurance AND add the legal protection insurance option
(check that this insurance covers landlord/tenant disputes - some may not
You may not need to add it as an option - a lot of solicitors offer insurance policies where you can use the insurance at any solicitor available under the scheme - just pop into one and ask)
This will give you a number to ring 24/7 for free legal advice
They may also write a letter to the landlord (its amazing what effect a letter from a solicitor will have, when the landlord realises you aint a pushover)
In worst case they may take up the case and sue the landlord at no cost to you

Are you via an agent or direct?
You are always better via a quality agent.

Chase again and point out they are risking damage to their property.
Also start by talking to citizens advice.