Some cards allow multiples of one thing to get elected, such as 2 planets.

Does each player place a vote for two different planets to elect this? Can one planet be voted on? Can people abstain?

I'm not sure what the official rules say about this, but I would personally conduct it as two separate "elect planet" votes, so everybody gets their full votes to cast for each of the two planets. Abstention is allowed, as always.

Thank you for your timely, omni-present assistance

Each player votes once, as normal, naming the two planets they vote for. Both planets get that full number of votes. Whatever two planets end up with the most total votes are the ones that are elected. You can always abstain from voting, but if you vote you would have to name two planets, you can't choose to vote for only one.

Indeed, this is confirmed in the FAQ:

Q: For “elect two planets” cards, does each player elect two
planets, or does each player vote for one planet and the planets
with the highest and second-highest number of votes are
chosen?
A: Each player gets one vote for a group of two planets. The
group of two planets that gets the most votes wins.