Can I use two different credit cards to pay for two different subscriptions on my family sharing apps and purchases?

Not easily. You would have to first ensure you have no personal balance that might be charged preferentially to another payment method. Next, you would have to keep changing the card order so the desired card was at the top of the list when an item was up for payment so that one was charged first.

Here's how to change the payment method order for your Apple account after Apple account balance (which will be charged first in all cases unless the item you are buying cannot be charged to account balance). For the first four steps, refer to the first image in this Support article Add a payment method to your Apple ID - Apple Support where it says to tap Edit to reorder or remove a payment method.

1. Tap on the Settings app.

2. Tap on the Apple ID section at the top of the page.

3. Tap on iTunes & App Store.

4. Tap Edit.

5. Tap and hold on your preferred Card and drag it to the top.

6. Tap Done.

Some people set up separate accounts (and probably also separate hardware) to split work and personal lives.

No. Only the card on your Apple ID is billed.