London - Oxford; reservations possible but not necessary.
Be aware that there has been a bridge collapse on the primary route from London Paddington which is closed until at least the end of May.
The alternative route from London Marylebone will be busy and does not take reservations.
London - Cambridge: no reservations possible.
3 and 4 no reservations possible, no supplement needed, whatever the app says.
Edit: IC Direct services are not high-speed. They use the high-speed line but at just 160 km/h.
Reservations on day trains are optional in the UK and as @Angelo says, they are free of charge.
Hi,
3 and 4 not mandatory
1 and 2 think also not, but you can do it for free at train stations in UK