Based on just the first half of your question I gather that you are not using the QB 'multi-currency' system.  If your version of QB includes multi-currency then you  should turn it on and start using it - that will resolve most of these issues.

If you do not have a multi-currency system then you have to manually fake it - which leads to the issues you find.

One workaround option is to record a foreign vendor bill as 2 separate bills - one bill for the actual amount in foreign $ and a separate bill for the exchange amount.  You can pay both bills with a single local cheque, any any apparent difference is leftover on the exchange bill - where it can be cleaned up later. This wont work well for inventory item purchases.

Another option is use single vendor bills and add a second 'exchange' bank account to pickup any differences.  If the vendor bill seems short then make a second dummy payment from this account to close it - it it seems overpaid then refund the difference into the exchange account.  Later clear the exchange account to FX exchange costs.