Can I store forms here in my account, that clients submit back to me?

You can create forms and that forms will be stored in your account unless you delete it. You can then share the form URL to your client and have them submit it.

Reference guide:

How to get form URL — https://www.jotform.com/help/401-Where-to-Find-My-Form-URL 

Account usage limit — https://www.jotform.com/help/408-Understanding-Your-Account-Usage-and-Limits 

Please note that Free accounts are limited to 5 forms only.

Let us know if you have any questions or if you need further assistance.