It sounds like your "Part 2" question may be answered using a Merge Field (Insert, Merge Field…) with, "<<FirstName>> <<LastName>" on the upper left of the form layout and, "<<Primary Phone>>" on the upper right.
As for your first question, I could suggest (I am very new to FMP) adding a global field for NameLookupFirst and NameLookupLast to the customer's table. I would then create another instance of that table related via the new globals and the FirstName and LastName fields.
By populating all of the customer information on the layout with the related fields, you should only see the information for the one related record via the relationship.
I assume this would give you a way to have a single record in your layout and lookup / modify any user's information via the two name pulldown menus (globals).
Just a thought.
To get your names to sort correctly by last name, then by first name, you'll need a calculation field that combines the two names.
We'll call it cFullName and define it as Last Name & ", " & Full Name.
Make this the field your value list uses to list member names.
You can then write a script to find your member's record:
Make your drop down list field a global text field (this is a field option you can specify in Manage | Database | Fields.)
in your script:
Enter Find Mode  // clear the pause check box
Set field [Members::cFullName ; Members::YourGlobaldropdownfield ]
Set Error capture [on]
Note: depending on how you've designed your layouts, a find may not be the right approach here.