Welcome. You seem to be in a pretty good position.
You might be best off posting this on the UK taxes board on MMM - it's not much about tax, in spite of the name.
On question 3, I would recommend taking a look at a world index tracker, such as Vanguard's VWRL - much better diversified than the fairly random mix of banks, oil and mining shares that dominate the FTSE.
I tend to agree with your comments on buying a house too, I guess it probably also depends on whether you're ready to commit to living in the same place for some years to come - not likely to have to move for work or other reasons.
Thought you could use your lifetime ISA to buy your first home - or have you previously owned one, so that is no longer possible?