These issues will not occur, if you will use Cedcommerce's Integration extensions. Your products, inventory, and orders will be fully synchronized between your Magento store and marketplace's stores. For example: if any item is out of stock on your Magento store then after synchronization, it will show the same on the marketplace's stores. Also, there is EndItem option, through which particular item will be removed from eBay and Amazon store.
You can also refer their user manual for the extensions:
https://docs.cedcommerce.com/magento-2/amazon-integration-magento-2-user-guide/
https://docs.cedcommerce.com/magento-2/ebay-magento-2-integration-guide-0-0-1/
So this made me stick to their solution cause it was just perfectly suiting to my needs. You can review at your level and take your decision.
If liked my solution, click Kudos.