Reservations are optional in the UK, mandatory on Eurostar and night trains.

Edinburgh - London: reservations are optional but recommended. Available for free on the LNER website.

London - Amsterdam: I'll have a look but most trains are likely sold out. Eurostar is extremely popular around Christmas + there's a passholder quota. Some options:

Option 1: 23rd December Eurostar London St. Pancras - Amsterdam Centraal 06:16 - 11:15 1st class only (43€)

Option 2: 22nd December Eurostar London St. Pancras - Paris-Nord 16:31 - 19:48 1st class only (38€) or 18:01 - 21:18 2nd class (30€). Mandatory night in Paris (not ideal).

Option 3 (the best one, no doubt):

• GreaterAnglia London Liverpool Street - Harwich International 06:45 - 08:11
• Stena Line ferry Harwich - Hoek van Holland 09:00 - 17:15 61.40€ incl. Eurail discount
• subway to Schiedam
• Schiedam - Amsterdam frequent train

Book ASAP option 3 to avoid getting stuck in the UK.

Munich - Rome: few routes possible. At least one mandatory reservation, supplement on the Brenner route.

https://www.seat61.com/interrail-and-eurail-reservations.htm

For London-Amsterdam, you could also consider a ferry. There's a discount on the base fare:

https://benefitsportal.eurail.com/benefits/stena-line/

There's still availability on around 22/12.

If you want to use Eurostar on 23/12, then book ASAP on www.raileurope.com (use "Add rail pass”).

Edit: ​@thibcabe was faster :)

Thank you so much ​@thibcabe I went along with option1. Thank you too ​@rvdborgt