How to restore a database, ignoring the free space within each file?
Is there a way I can restore this database ignoring the free space in each file?


No you cannot. You can restore the database and then do a shrink of database file.

I assume that you are aware of all the caution that the smart people have given.


I Need to Shrink My Database - I just freed a lot of space
Why Does the Transaction Log Keep Growing or Run Out of Space? - since you have a large ldf file.



  Basically I will use my "new database" to develop and test something, I would prefer to keep it small.


Why dont you use a data generator or from here or just get a sample of data from your PROD for testing ?