wazz:
Can I tell them when I can and can’t work etc?
Yes, absolutely yes. This is the main selling point for Agencies.
And don’t be drawn into a “Why not”? scenario. They do not need to know why you can’t do a shift for 'em.
A simple “No, sorry, not available that day” is plenty.
I mention this because it happened to me in my early days of puddle jumping (9 months back 
) and I look back on that phone call with much embarrassment