To your first part about seed starters;
Seed starters don't really contain any nutrients. The reason for this is because seeds are very sensitive, nutrients could actually burn and/or kill the plant. Once the plant grows you can repot them into "normal" soil that does contain nutrients as it does need them to grow. In saying this, things like compost are still recommended not to be spread against the plants (even well established ones) as it can burn the stem.
Potatoes tend to start growing from the 'eyes'. Soaking a potato (or any vegetable for that matter) usually makes them rot rather than grow. This does not mean it's impossible and it can very well be done. It depends on the purpose you are doing this for. Most people that like doing that are growing it decoratively (yes! People actually grow potato decoratively), or as a learning process where you can see what happens.
Composters do need at least some moisture to help decompose whatever is put in them. Alongside it's recommended to have certain parts of green and brown (I believe they call it?). I'm not entirely sure as I am yet to start composting myself.
You do not have to wait to use dead clippings, they can be used fresh! Just try to make sure there are no seeds in there as they might germinate and grow weeds wherever you composted. There are probably ways to avoid the seeds from germinating as well, perhaps because of the heat of composting. I can't confidently give you tips about that though.
From what I know (and do myself) is almost completely fill the beds up. Maybe leave about 4cm to avoid overflow when watering. This is because of sinkage; this happens naturally. You can combat this in some ways, but regardless it often requires us to top off the bed after the growing season as well.
If you are using (fresh) manure in your beds, make sure it has time to break down before planting in them. This is because manure generates a lot of heat, which essentially can burn your plants and their roots.
When using compost in established beds, make sure it's spread around the edges of the raised bed, keeping a fair distance between the plant and the manure. This prevents the plant getting damaged. The roots of your plants can still reach for it as it gets watered in as it's still in the same bed.
Potatoes turn green when exposed to the sun. Do not throw those potatoes out though! You can always replant them and grow more from them; the new growths are not poisonous.
I loved seeing what you've got going on!
