does the board decide what position each officer holds

Typically yes unless your bylaws or cc&r's state otherwise.

Your homeowners vote for those on the board and then those who win actually vote each other on or delegate the roles. It is a misunderstanding that people vote for someone to be a "president"

This really belongs in your bylaws. If it isn't there, you might want to be sure it isn't spelled out somewhere else. Check your Declaration or CCRs, and any statutes governing HOAs or non-stock or not-for-profit corporations if they apply.

In most cases I'm familiar with, association members elect the board, and the board elects its officers. Notice I said elect. It's imprortant you do it this way and not just come to some informal agreement. What's the next board going to do? You might also get a copy of Robert's Rules and read up on how organizations are set up and boards and officers are elected. By the way, it may not be necessary for all officers to be board members. Generally, the president and vice presidet must be board members, but sometimes you may want to be able to elect someone who is not a board member (a homeowner or even an outsider) to be secretary or treasurer because of some expertise they might have. Of course, such people should be willing to volunteer. Also, in that case, these people may be officers but they are not board members. That means that although they can attend meetings, they cannot participate in discussions, make motions, participate in debate, or vote. They can give reports or answer questions, but 2/3 of the board has to vote to agree on this.

I find it unusual that the number of Board members is stated, but not how the officers get placed into their positions . . . .