What next for my seedlings?

This is my first full year growing my own I and have trays of red cabbage, leek and onion on the kitchen window sill which have all germinated now.  I now need to free up the window sills for my next batches of seeds (savoy cabbage, tomato)

Can I move the seedlings outdoors during the day and pop them in the shed overnight (I plan to construct a cold frame but haven't got round to it yet)

If I move them outside should I avoid direct sunlight or will that be ok?

How long before they are hardy enough to be left outdoors 24/7?  Not having a greenhouse, plus my sheds been taken over by kids toys, I have limited space and it involves a lot of juggling and moving things backwards and forwards, which is a bit of a pain.