Why is it לנשים and not הנשים ? Is that required when describing possession? What is the rule and when must you use it?
Yes exactly. The ל is required to indicate possession. It comes before nouns that have (יש) something
In Hebrew you write the amount of things according to their gender. 16 can be שש עשרה (fem.) or שישה עשר (masc.). Since hat (כובע) is a masculine noun you need to say שישה עשר.
Btw what you wrote (שיש עשרי) is incorrect spelling in Hebrew , you probably meant שש עשרה (fem.) since it probably sounds the same.
Hope it helps :)