What can I deduct if can't agree with my wife

Me and my ex were married on the last day of 2023, and divorced on Jan 2024.

for 2023 tax, If we file separately, how can we determine who get to deudct what?

 

1. We have two dependent children, our divorce agreement says each of us can claim one child. but it didn't say the timing, I just assume it's for after the divorce. so for 2023, I think I can claim both since I have a high AGI (based on some rules I read online). is this right?

2. We co-own a house, she's the only one on the loan. she's been paying mortgage so the 1098 have her name only. she says she can deduct all of the interest. however I researched and it seems if we are in a community state, such interest should be splitted equally so each of us can deduct half. is this right?

3. we also have property taxes, if we can't agree, can I claim half?

4. we have some shared account which has dividend and interest, she just says she won't report any. I don't want to be the one bearing of tax liabilities for these. is it safe for me to just report half of the dividend income?

In general, if we can't agree I think I will go ahead claim half of everything. If we can't agree with each other and went ahead file tax our own way (e.g. each of us claim two kids as dependent), will we  be in a big trouble?