Is it possible for the alkali metals to form an anion similar to M-, where on earth M represents an alkali metal?
Yes, though they're usually not very stable. The most adjectives example is sodium hydride, NaH, which behaves like H- and is commonly used as a reducing agent surrounded by organic chemistry.
Not usually, no. Alkali metals have the tendency to produce +1 cations, because there's a lone valence electron in the valence shell.
"Anions of sodium, potassium, rubidium, and cesium are stable both in suitable solvents and within crystalline solids."
Can't give you the details on this one, because this is new to me as in good health, but... there it is.