Yes, the micro:bit processor in the Hummingbird Bit and Finch Robot 2 is the standard micro:bit V1 that you find elsewhere, so you can use your existing micro:bit with either product.
The Finch Robot 2 and Hummingbird Bit are also compatible with micro:bit V2.
When using Snap, Python or Java with Hummingbird Bit and micro:bit V2, you must use a bluetooth connection to connect your Hummingbird Bit to your device. A USB connection is not supported when using micro:bit V2 and the Hummingbird Bit. If you are using a Windows computer you will need a BLED Bluetooth Dongle to connect via bluetooth. Connection via USB is supported using the MakeCode programing language only.
Both the Hummingbird Bit and the Finch Robot 2 do require a micro:bit to work, so if you do not already own a micro:bit you should purchase one with your robot.
The power behind the BirdBrain tools + micro:bit connection is that you get two learning tools combined into one! You can use the micro:bit to do separate projects that you would find on their website, but you are also able to take your learning to the next level by adding external components and multiple programming languages with the BirdBrain robots.