Can I remove the branding and am I able to host forms myself?

Hi,

It seems that your Jotform account is in our free plan. Because of this reason, the Jotform brandings cannot be disabled. You should upgrade your account in order to remove brandings:

How to Upgrade My Account

Also, you can host the form files to your own server by getting the full source code of your form. Please check our user guide to see the details:

How to get the Full Source Code of your Form

If you need further assistance, please let us know.

Regards.