Hi @manzin. Thanks for being part of GoDaddy Community! In general, you should be able to accomplish what you're trying to do by using our domain and email forwarding service. However, things could get complicated in a few scenarios.
In regard to forwarding, please keep in mind that our forwarding service does not accept HTTPS requests. If your old.com site is using an SSL Certificate and HTTPS now, that may complicate things for you. If you use our forwarding service and someone tries to visit https://old.com, that will not work. However, if you're not currently using that protocol, you shouldn't need to worry about it.
In regard to email, our free email forwarding plans are part of our Workspace Email environment. If you're already using Workspace Email, you can't set up a forwarding email plan for an address that is an active Workspace Email account. You'd need to remove that address from the email plan before you'd be able to set up a forward for it. If you'd like to keep the plan active, you can create a CC forward instead.
Also, if you're not using Workspace Email currently, you'll need to make sure you update your domain to use Workspace Email MX records. For a US plan (common), this would be:
Obviously, if you plan to cancel/delete an email plan, make sure you back up any important emails or contacts first.
JesseW - GoDaddy | Community Manager | 24/7 support available at x.co/247support | Remember to choose a solution and give kudos.