Plants grown slowly in a cold frame over winter that have been subjected to winter frosts would be able to cope with severe frosts now. How you have yours that tall with side shoots after 6 weeks is a mystery. Mine were sown early December and are half that size. If you have grown them inside then you need to leave them outside for a week or so in the cold to acclimatise them a bit before planting. If they have been in a coldframe then no need to do that.
Provided they look healthy and nice and green then no fertiliser is needed. Open up the rootrainer and check what the root system looks like. It needs to be nice and full before planting out.
Mine were planted out last weekend.

Maybe it's a bit longer than six weeks but not much - I think I sowed them mid Feb. I pinched the tops out as soon as they had 2 sets of leaves and the side shoots appeared within days. They were grown on a windowsill but are now in my neighbour's unheated greenhouse. They look very healthy! I will give it another couple of days & then put them in the ground. Thank you very much for your full reply!