Can I attach a Thunderbolt-to-Firewire adapter and a Mini DisplayPort monitor to the same computer? I have a 2013 MacBook Air with one Mini DisplayPort/Thunderbolt 1 port. Is there a way to connect both an LED Cinema Display and my old Firewire accessories to this port?
You need a Thunderbolt Dock with a Firewire port

Thunderbolt is not like video or USB where you can get an inexpensive splitter and just multiply or split the signals.   So, to use two devices simultaneously, you need a dock.