Cascading Dropdowns w/ Add New, etc., etc.

I have 3 record types:

Company

Branch

Contact

Where Contacts belong to Branches which belong to Companies.

Question 1:

On the form for Contact, I want to be able to choose which Company and Branch the Contact is being created for. I got this working by filtering the Branch lookup dropdown as so:

input.Companies.Company_Name

However, if I allow new Branches to be created from the dropdown with the +Add New button, I need to ensure that whatever new Branch is created is related to the Company picked in the Company dropdown.

This seems like a pretty common pattern. How do I do this?

Question 2:

On the Company form, I have added a Subform to list Branches related to this Company. I've also enabled the +Add New button for the subform. My thought is that when someone is Entering or Editing a Company record, they should be able to add Branches (and Contacts) to the Company at that time, without having to go and build the Branch and Contact separately. (In fact, I intend to hide the Branches and Contacts tables so you can only see this information from the Company form or view.)

When I click +Add New, the form that pops up to create the new Branch has a dropdown for Company. I want this dropdown to default to the company from which I am adding the new Branch. In fact, I would like the Company dropdown to not be shown at all (only fields that are Branch specific).

Again, this seems like a pretty normal pattern. How do I do this?

Thanks!