Like others have said, "with" implies a two-way conversation, while "to" does not. However most of the time they're used interchangeably. The only time when the distinction is important is when you're talking about inanimate objects. "He's talking to a tree" means he's simply saying words in front of a tree. "He's talking with" a tree means the tree's talking back! Someone insane might talk to a tree, thinking they're talking with the tree.

When you're talking about people, it doesn't really matter which you use. If you said "She was talking to me" I would assume you were having a conversation, unless you put a lot of stress on 'to' ("She was talking TOOO me" implies that she was the one doing all the talking).

Speak is more formal than talk.

We usually use 'to' after speak and talk.

In more formal situations, people sometimes use 'with' (it's more polite because it suggests a discussion rather then a one-way encounter):

- I need to speak to you about this conference next week. (I have somehting to say)

- I was talking to Richard Moss the other day about the golf club.

- May I speak with you for a moment? (rather formal)

I think it depends on the context. Speak with implies a conversation whereas speak to is more a one-way speech in which you talk and another person just listen to you.

Agree with the people above me, but I'll add that I think "speak to" is also used quite regularly for two-way conversations.

And maybe a question is more appropriate for this than a discussion.

both are correct.  It personal choice.
usually, I have tendacy to say "speaking with"  (present tense situations) and "spoke to"  (for past tense situations)