Does flying into a military airfield have any security implications?
Obviously
Do they ask what your purpose is when visiting?
Yes
When you guys have been in to Lyneham, Brize etc....what is there to do?
No more or less than any other airport - in fact if you are going for coffee and cakes a lot less. There is no point going to a military airfield unless you have business or pleasure outside the airfield in mind, or some specific purpose on the field (visiting a museum).
Any facilities? (car hire etc)
Rarely.