In general, items made from GEM yarns don't need any more special care than other handknit items, but here's a quick overview to help you get a long and happy life from your finished object.
When you get your yarn it should have a little label on it which says either 'hand wash' or 'machine washable'. If it says it's hand wash only, this usually means that the wool has not been superwash treated and may therefore felt in a washing machine. The three things you need to avoid combining when washing these items are heat, agitation and soap. One at a time is fine, but all three will cause the item to start to felt. If the wool has been superwash treated, you can put it in the washing machine - I recommend a cool cycle to be on the safe side.
I've tested my acid dyes and the colours are safe in a normal 40 degree colours wash.
Blocking is much less scary than some people make it sound but it really does improve your knitting. The idea is that you shape the item after washing - just like you style your hair after you wash it. I usually just wash and rinse my item, lay a towel or a board down on the floor and spread my knitted item out into the shape I want it to be when it dries and leave it. Lacework in particular may need to be pinned to stretch it out and you can buy sock blockers which you can put socks onto to create the perfect sock shape, but they're not essential.
Natural dyes are a great option for the eco-conscious. I use Earthhues natural dye extracts twinned with organic merino wool for my Earth range. These products will need to be hand-washed - not because of the dyes, but because the yarn and fibre has not been superwash treated. I've heard rumours of natural dyes not being colourfast enough or fading in the light, but I've not had these problems with the dyes I use. Colours may fade on an item left in bright sunshine (on a windowsill for example) for a long time, but the same is true of chemical dyes. I have done a couple of lightfastness tests and the dyes I use do fare almost as well as my acid dyes..
I know that there is a lot of conflicting information out there about natural dyes. I personally believe that they are a great option if you want to try something new with your work. I don't use any metals (just alum as a mordant - which is used for water purification among other things) and I make an extra effort to use as little water as possible when using natural dyes. The dyes themselves are from plant or mineral extracts and sourced in such a way that they support small local economies, so may be a good option if you are looking for a way to be more earth-conscious with your work.