For identifying whose lamb is whose, we use turkey wing tags, like little metal padlocks, which are applied by hand and can be re-used if sterilised. We keep careful written records, then we put in the proper tags at weaning. The lambs will be next to their mothers so it's easy to tell who's who, unless someone has stolen someone else's lamb - they are good mothers but can sometimes get carried away with enthusiasm
We have found that marker spray is licked off.
Hebs usually have no problems lambing but that cannot be guaranteed so you should check them as often as you can, and as Anke says, you should be prepared to stay to assist if there is a problem. It doesn't take long for a ewe to die and far less time to lose a lamb.
We would normally check our ewes every two hours during the day, with more frequent checks first thing, and about midnight then 5am.
Hebs are easy to catch for about the first 15-20 mins of life then they are off - you get good at rugby tackles, while avoiding squashing them
Our Hebs lamb in the fields, but have access to field shelters, which are made of four corner posts, wooden siding on 3 sides and a tin roof, well attached. We put straw in these and top it up if a ewe has lambed inside. Some will lamb in the shelters, some out in the wind, but the lambs are usually ok as they have very thick birth fleeces. Having said that we did lose a lamb in a severe storm last spring.
Particularly if you work, it is worth trying to group your lambings, so you can arrange two weeks annual leave each to cover it. We put our tups in with their ewes for just 4 weeks - last year all the lambs were born in the middle two possible weeks, but that cannot be predicted.
Hebs apparently don't take too badly to lambing indoors, but there are dangers of pneumonia, post-partum infections, mis-mothering and stolen lambs. We always have an emergency pen set up inside (in our veggie polytunnel), ready in case of emergency with straw, water and a closed bucket of food- it can be a disaster if you are on your own in a blizzard, trying to persuade a ewe to follow the two slippery lambs you are hanging on to, then finding you have no pen when you get there. Most years we don't need the pen, but we always set it up.