Do we file only once a year, or are we required to file quarterly?
Who are "we"? Partnership? Files annually. Partners? Depending on your situation, quarterly estimates may be required.
When am I required to fill out and submit a 1065?
Within 4 months and 15 days after the partnership's year-end. If all the partners are individuals, that would be by April 15th of the next year.
Does each partner fill out their own K1, and if not, who is responsible for doing it?
No, K-1 are part of the partnership's informational return to the IRS (Form 1065), copies of which go to the respective partners. The partnership is responsible for doing it (and each of the general partners, as being responsible for the partnership).