The correct answers are we are throwing a massive party for Alex and I am renting a food truck for the event.

"We are throwing" and "I am renting" correctly use the Present Continuous to describe a fixed plan for next weekend.

"We throw" is the Simple Present, which sounds like a regular habit rather than a one-time future plan. "Need" is a stative verb, meaning it expresses a state rather than an action, so we generally do not use it in the continuous form ("I am needing" sounds unnatural).