The से is a "postposition" which has an effect on the noun-phrase (my friend) that proceeds it. It puts the noun-phase into the "oblique case." The "oblique case" form of apna is apne. The oblique of dost is dost (no change).

No chahiye would mean something else here. mujhe karna hai = I have to do. Same construct with any verb, if you are saying that you have to do something, use mujhe (infinitive form of verb) hai. mujhe karna chahiye = I should do.

Because it is दोस्त and not दोस्तों

I meet: मैं मिलता हूँ, I have to meet: मुझे मिलना है. For 'Have to do' forms of a verb, you use object pronouns (like मुझे) instead of subject pronouns (like मैं,) and the verb goes into its infinitive form, मिलना, instead of conjugating it at all. Then है finishes the sentence. I eat food: मैं खाना खाता हूँ. I have to eat food: मुझे खाना खाना है. (खाना means both food and 'to eat')