I set my dad's Apple Watch with my iPhone, can I call him?

If you set him up as an independent cell watch using the Family Sharing technique you should be able to call him. If you set him up using your iPhone he has the same number on his Watch as you do on your iPhone.

Set up Apple Watch for a family member - Apple Support

There are two different numbers for an Apple Watch. If you set it up as say a normal watch for you it syncs the same number to the Watch, any call to your iPhone will also ring on the Watch. The other number is for billing purposes. On some carriers (such as AT&T you can also call this phone number but outbound calls will use your iPhone number. If you set up his phone as described in the link I provided it will exclusively use the Watch phone number and he won't get your calls.