Q1: Not as far as I know. It doesn't cause damp but it may contribute to an already poor situation. Before an installer installs, he used to have to undertake a simple survey to assess (amongst other things) the exposure factor of each external wall. A westerly-facing wall in an exposed and windy location might not pass. The reason for this is that CWI prevents air circulating in the cavity, and in some cases can assist the water in the outer leaf to transfer across the cavity ties into the inner leaf. This happens if the metal cavity ties do not have the mortar removed that drops down onto them during construction (it should be removed by the brickie as it happens). The way I have seen as then cause a problem is by a damp patch about a foot in diameter in very wet weather showing on the inside centred around the offending tie.
Suggest you seek advice from your proposed installer.
Q2: No, it is surely a capital improvement, not maintenance. Would you expect the leaseholder to fund double-glazed windows? However, in view of the cost-savings to the leaseholder you might be able to negotiate a contribution.
Q3: No. Though ask the installer about what it would do in the unlikely event of damp penetration - it should be part of their warranty.