In answer to your second question, can other owners vote against someone being on the EC, that depends on the number of members of the EC, as determined by the owners at the AGM.
You can have up to 9 members of an EC. The owners have to vote how many they want on the EC, and that can be any number up to 9. For example, if the EC decides that the EC should have 5 members and there are 6 people nominating to be on the EC, then it comes down to a vote. The person who gets the least votes will not be on the EC.
That is slightly different from voting against someone, what you are doing is voting for someone else in preference to them.
If the owners determine that there should be 7 members of the EC, and 7 members nominate, there is no need for a vote and they are all EC members.
If you want to keep someone off the EC, what you can do is agree with other owners to have a certain number whereby you know that you can exclude a certain person who may wish to nominate, providing you are certain you have the votes. That is what Jimmy is referring to, and I agree however, it can work both ways. We have one owner here who is a total pain in the neck, and having him on the EC would be an absolute nightmare.