1. Some British speakers say "shall", but this is now considered a bit old-fashioned; many speakers now prefer "will". In American English, "shall" is quite rare.
2 (and 3). "Four stars" is a so-called noun phrase; it's made up of a headword (the noun itself, "stars") and a modifier (here, the word "four"). In the phrase "four-star hotel", it is no longer a noun phrase but an adjective.
In English, when a noun phrase is converted to an adjective, we put hyphens between the elements and we make the noun singular (that is, we drop the plural marker). Some more examples:
The girl is four years old. She is a four-year-old girl.
The man is six feet [about 180cm] tall. He is a six-foot man.
This process uses four colours. It is a four-colour process.