Yes, you can use marmite to make a hot drink if you want (I wouldn't )
I believe marmite came first. Vegemite started being made when the marmite imports stopped during the war (although I can't now remember if it was WWI or WWII)
Marmite doesn't go off so the Olympic jar would be just fine. (I've just finished a jar which had a use by date of 2002, it was absolutely fine.)
I understand from my US based expat. friends that you can buy it on Amazon, but only in trays of 24 jars at a time, which is quite a commitment!
(and do check YouTube for Amanda Palmer's 'Vegemite (the black death) song)