Yes definitely , landlord insurance is different to buildings insurance. I'd recommend legal cover as an add on too.

You need to check out what’s included in the building's insurance that’s included with the service charge.  I have a similar leasehold flat, but for leaseholders, the included building's insurance only covers the exterior of the flat, not the interior.  So it doesn’t cover restoring any interior work and fittings, bathroom, kitchen, decorating etc.  As others have said, you need to get your own landlord’s insurance and make sure you include legal cover.

You need landlord insurance and you should put a clause in the AST that the tenants must have contents insurance before handing the keys over

Yes. I have landlord's insurance for my leasehold flats, all of which are covered by a block insurance policy for buildings insurance.

In a leasehold the insurance from the freeholder is only buildings insurance. It doesn't cover the contents of your flat so you should already have insurance in place for that for your personal possessions and fixtures like kitchen and bathroom. If you don't have that now then that's a huge risk. You need the same for when you rent it out but the landlords version. You may also want rent insurance. The tenents will need their own contents insurance for their personal possessions.

Yes. You need landlord insurance. The clue is in the name.