As a PPL(H) student, if it is exercise 25, I log it as cross country.
As regards landing away - for the qualifying cross-country, my flight school requires me to get my log book signed (I don't think this is a strict CAA requirement but seems good practice in case queries are raised is there is an audit). In any case, there is also the landing fee to pay. I think if I hovered over to the tower and tried to do either of these without putting the aircraft down, switching off the engine and getting out, my instructor might ask serious questions about my suitability to fly!
As regards currency to carry passengers - if I was that low on flights in the last three months, I think I would be asking for a check flight before carrying passengers rather than worrying if bouncing the helicopter from ground to hover a few times would count!
Matthew