Μέσα and σε commonly go together.
1.Μέσα + σε + άρθρο (article) = in a
exp. Το έβαλα μέσα με μία τσάντα - I put it in a bag
2.Μέσα + στο (and all its other forms) (For defiinite object) = in the
exp. Το έβαλα μέσα στην τσάντα -I put it in the bag.
3.Μέσα all by itself, but in general cases = in/inside
exp. Come in! - Έλα μέσα!
I think I've covered everything! ^.^
Um, not sure if that would be grammatically correct. inside of is used as a noun, but there needs to be something to indicate so.
For example, the inside of a house -Το εσωτερικό ενός σπιτιού. (there is a the for the phrase to make sense.)
So, if you wanted to use it like so, maybe "The water is on the inside of a glass" would be a bit more correct? ^.^
Hmm, I disagree. I'm a native speaker of U.S. English, and "The water is inside of a glass" is the first thing that I would think of: in fact, it is what I wrote. Omitting the "of" also sounds perfectly fine to me, but I don't think that it's necessary.
As you say, in the phrase "the inside of a house," the word "inside" is a noun. But here it is not: "inside" is a preposition, and "inside of" is a prepositional phrase.
Σε only means σε but is translated as in/to/for/on/you depending on what the proper translation in the English phrase is. ;) Imagine how difficult it is to go from Greek to English with those translations for a Greek speaker... (well, 'you' is easy.)
Also, there's no need for shouting.