Welcome to the forum.
Yes, you can use external drives with an apple MacBook Pro.
No, you don't HAVE to format them, as the Apple operating system can read (but not necessarily write) to Windows formatted drives. macOS can read all formats, but cannot write to NTFS formatted drives. There are third party drivers that allow macOS to write to NTFS drives, the one recommended here is ParagonNTFS.
New MacBook Pros do not have optical drives. Yes, an external optical drive will work.
Yes and No on the App store. I have some from the app store and some directly from developers.
One thing to note is that the new Apple machines all use USB-C, so you will need an adapter to use older USB drives and optical drives with the newer portables.
One more terminology: there are two types of portables sold by Apple, the MacBook and the MacBook Pro (usually abbreviated MBP). You can find them both at apple.com.