1. Does anyone know how big the root is on a well developed Euphorbia myrsinites? I am trying to figure out how much root space
is needed and where I can put it.

2. Cutting old stalks that barely have leaves on them encourages the plant to form new stalks?
I have some in pots which have some stalks that barely have any leaves on them but they are like 10 inches long, leaves for about 1/5 of that lenght and i see small stalks full of leaves at the base growing now, about 5 stalks that are 2 inches long.
I was thinking to cut those old flowered stalks with barely any leaves on so the new ones get the energy instead, however I am not quite sure if the plant would not then divert the energy into blooming those new small stalks basically stop growing?

These are most often propogated by division but you can take cuttings in Spring as well. I'd let them dry for a couple of days or seal the ends with a flame. Take care with the latex as it can irritate skin. You can put the cuttings into seed compost or similar.
As for the roots I'm not sure how large the system could be, they would probably fit the space alloted to them I imagine, I've seen them growing at the top of walls and rockery beds where there isn't a lot of space.
You can certainly cut off the old flower stalks and this will encourage new growth from the base.
Good luck with this exceptional plant.

Thanks for the reply, I've cut 6 old stalks with flowers with barely any leaves on them, and yes, that latex is sure there now that i've seen it, definitely can't miss it as it oozes quickly in pure white.