At a Members Meeting of an HOA, can homeowners make motions on certain issues and ask for a vote?

It depends on the By-Laws of your HOA.  Most HOA's allow members limited control which is to elect or even replace the Board of Directors.  It is likely that if you want to replace the board members outside of the annual meeting held for that purpose you will have to obtain signatures from a sufficient amount of members to demand a special meeting of the Board with an agenda item of a recall election. If you are not familure with the process you will be well advised to contact an attorney who can lead you through the process.     Good Luck!