A few questions financial aspects of live aboard cruising....

I am English and plan to buy a US registered liveaboard boat in US. Although
I intend to spend time in US waters and Caribbean initially, What is payable
if I enter EU waters for a limited time and then leave, is there a time
limit? Also are duties payable when I visit any other world cruising
grounds?

I intend to keep a small flat in England, what is the tax position if I am
living away from UK for most of the time? Again, are there time limits etc.

Can I still get my state pension paid if I am away from UK? Is there any
angle to maximising this position etc?

Thanks in advance for your advice.

Ray