It's very hard to prove predetermination. You basically have to admit it and, for any action to take place, some proper evidence, like an email that says "No matter what, I'll do whatever I can to make sure it happens!". Even if that's the case, would one councillor being predetermined typically "swing" a vote? If no other Councillor is considered predetermined, then they have come to their own determination meaning the arguments for voting that way are reasonable (which the predetermined Councillor can latch onto). If no other Councillor is swayed by the arguments for voting that way, it's 1 vs everyone else, so the pre-determined Councillor doesn't get what they want anyway, so it's not a problem there either.
With regards to your written proposed agenda items, any Councillor who is proposing anything has a predisposition on the matter - they wouldn't be proposing it otherwise. You can enter the room predisposed on an item. You likely do it with every other item on the agenda; you are told about them days in advance so you can research and form opinion after all. Absolutely nothing wrong with that. Predetermination is when you are determined to vote in a particular way, no matter what argument is put up against you. So as long as your second for a written proposal (and is reasonably considered "predisposed") is willing to consider the alternative arguments during the meeting, they shouldn't be considered "predetermined".
I would argue that technically you can be the proposer of something that you have an interest in. For instance, you might not reasonably realise you have an interest until the discussion begins in which case you must not speak further on the matter and (probably) remove yourself from the room. Even if you know you have an interest, you can still "move the motion" prior to leaving the room - you just can't speak on the matter. Having a second here really helps, because they can take things forward in your absence.
Again, technically, any motion should be proposed and seconded prior to making it on the agenda, it probably should be noted on the agenda who is the proposer/seconder too for the Chair to properly introduce the item and open the debate with the proposer commenting why the motion exists. I think a lot of this has been done away with for the sake of convenience (i.e. if it's on the agenda, the clerk has decided it's legitimate business), but it's all too easy for the Clerk/Chair/VC combo to become "the power".
If you're having issue getting an item on the agenda, don't forget SO 9h - rejected motions shall be recorded with an explanation by the Proper Officer of the reason for rejection. Take it back, correct it, resubmit. They can't argue against it forever.
Good luck!