Yes, you can certainly achieve this. Just navigate to Settings >> Payment Gateways (under Billing section). Now click on the gateway to select the card logos as given in the screenshot below.
The checked logos will be displayed on the checkout pages for which that gateway is set as the default one to store cards. For more information on this, refer to our document on smart routing.
1) This option is only to select the card logos displayed and does not mean the payment gateway will accept only the selected card types. You would have to get in touch with the payment gateway to know which card types are accepted for your gateway account.
2) This is applicable only to V2 checkout pages. This is not applicable for V3 checkout pages.