My answers:
- the size, color, and condition of stem are good indicators. I have not grown SS myself, but I have seen them a lot, have cooked them few times. The color should be yellow.The stem get brown.
-- green spots may mean not quite matured.
-- put them on dry straw, hay in cool ventilated place.
-- I do not think you can freez raw squash.
-- I think your friend is right.

note: SS is very sililar to shark fin melon.
Shark fin melon can be harvested and cooked (in soup) from young to mature stages.Mature ones will get hard seeds, hard rind, and more pronounced strands. Younger ones will have soft (edible) seeds that need not to be removed before cooking.
Also I wash them well, cut them into pieces(chunky) cook them(in soups) with skin on.

Spaghetti squash is a winter squash in the C. pepo species. They need to be mature for best results. Like any other winter squash they can be picked when the skin is too hard to dent with a fingernail. There are several cultivars which range from a yellow-tan to striped, so it is difficult to judge from color in general. In essence it is a stringy C. pepo. The flesh after boiling or baking is pulled apart and makes a decent spaghetti (pasta) substitute. Some folks do freeze winter squash, but the changes in texture are not to my liking. Store in a cool dry environment just like an acorn or delicata type. They are not great keepers like the C. moschata or C. maxima group but keep as well as an acorn.