Admin - ill defined and sometimes synonymous with reception work, but I'd say more emphasis on organisation/systems and less on customer service. I'd highlight computer skills, particularly in Excel/Access, if you have them and any time you've created systems for organising something, including in a volunteer capacity.

Not because I'm particularly suggesting you work for them, but because they do do ridiculously detailed job descriptions, take a look at the jobs here for things that might be included in an admin position.

Re (3) - I think they do, if I remember correctly.