@Lee_Rigby the forms you create are all shown on the homepage of Forms unless you have collaborated with others in which case they are saved in the Group forms tab. However I would suggest that you create a SharePoint site, possibly with just the homepage and that you add the Forms web part to that page. Your users won't need to know the long url of the form but can just go straight to the SharePoint site.
You can also use a list on this SharePoint site to store the responses. You will need a column for each question. My forms are always just within the organisation so I use the Title column of the SharePoint list to store the email address of the responder.
To ensure your form responses are sent to the right department automatically you will need to create a flow in Power Automate. This will get the form response and then there will need to be a type of condition called a Switch which looks at the department name selected by the user in the form. This condition is in the form if department is equal to.... then..... You would have a case for each department with the email action in each one sending it to the correct department. There are other ways of selecting the department, from a separate list for example, but the Switch/Case approach is a good way to do it providing you don't have more than 26 departments.
At its simplest, the flow would look like the one below, saving the form response to the SharePoint list and sending the email to the appropriate department.
Rob
Los Gallardos
Microsoft Power Automate Community Super User