I'm trying to add a custom form by adding a webpart. I've noticed that when I click on the list tab > "form web parts" > "default edit form", it goes straight to the edit form and not to the section where I can add a web part.
Why is that happening?
That is not how you add a form webpart. That will just redirect you to EditForm.aspx. Instead try this:
Edit the page -> Add a page viewer web part by clicking on Add a web part. Once you've added the page viewer web part, edit the web part to show this URL: http://siteUrl/Lists/ListName/EditForm.aspx
?ControlMode=Edit&DisplayMode=Design to force it to show edit mode.