1) As the flight from Manchester will be long, is there a type of ticket or rover we can buy in advance, so that we don't have to faff about after immigration and can just jump straight on the first available train we see going?
At Airport station, you can get on the train without a ticket as there are no barriers. You are able to pay on arrival at the customer service counter (card accepted) before passing through the barriers. In this situation you would get a physical ticket which additionally gives you one free local journey on the MTR.
Alternatively you can buy e-tickets for the Airport Express online from the MTR website. You can do this after getting on the train, as there is normal phone signal in tunnels in Hong Kong, as well as free wifi on the Airport Express.
You can also buy discounted e-tickets from Klook (like a Groupon for Asia):
https://www.klook.com/en-GB/activity/71-airport-express-hong-kong/ However when I have used this website, the tickets took around 30 minutes to arrive so you should buy as soon as you have internet access after landing. Other discount websites and apps are available too.
2) Can you get a rover or a pass for 7 days that includes tourist attractions such as maybe discounts on the Peak tram?
Unlike in some European cities, there is no tie-up between tourist attractions and public transport.
Public transport generally functions on a pay-as-you-go basis as the fares are low by first world standards.
There used to be an Airport Express return ticket with 72 hours of unlimited MTR travel included, but this is no longer sold. It was marginal as to whether this saved money.
There is now a Tourist 24-hour Pass, which you can buy in advance online, but must collect a physical smartcard at an MTR station. It costs HK$65, so it is only likely to be worth it if you are travelling to distant parts of HK by train that day. It is valid on MTR trains and the Light Rail, which is a tram system in the northwest of HK, as well as the Light Rail feeder buses. It is not valid on the Airport Express, to/from the mainland border stations, or on regular buses or the Hong Kong Island (double-decker) trams.
There is also a One Day Pass for $29 valid from Nam Cheong station and further northwest on the Tuen Ma line + light rail. This may be useful if you want to spend a day bashing the Light Rail network, although depending on where your hotel is the Tourist day pass may be cheaper.
As of tomorrow, 23rd Dec, you can use VISA contactless cards and devices to tap in/out for MTR heavy rail journeys, except the Airport Express (as mentioned you can already pay by card, but you still get a physical or e-ticket). There is no daily capping. Mastercard will not yet be available by March 2024.
VISA and Mastercard contactless payment is already available for most buses in Hong Kong, as well as the Hong Kong Island trams. Therefore you may not necessarily need to buy an Octopus card, especially if you can use the app.
The Octopus card is not exactly an equivalent of London's Oyster card. In the original implementation, Octopus is basically electronic cash, as it was anonymous and could only be topped up with cash (in multiples of $50). Many merchants, not just transport operators, have Octopus readers which helped to reduce the need for coins.
The anonymous version is still available and is still the case for tourists using a physical card, but residents may use personal Octopus cards for things such as a building entrance/lift fob and collecting government subsidies.
The Peak Tram is a private railway. Tickets can be bought in advance on their website. Klook etc appear to offer discounted tickets and various combo tickets for other attractions.
Hong Kong is very cashless, I don’t think I had any over 3 days, but could have got some if needed.
Hong Kong is extremely cash-based. While a tourist sticking to the central commercial areas may be able to use a bank card for everything, it is not unusual for large purchases, bills and money transfers to be paid using cash. It would be strange for a merchant not to accept it and a substantial proportion of the average shop's transactions can be expected to be conducted in cash, even if they accept Octopus, bank cards and the QR code payment systems.
For a tourist the main reason you would want cash is for taxis. Some taxis have Octopus readers but they are reluctant to use them. Having cash would also be advisable if you want to venture away from the central areas.