another question, can we record the chroma keying video(realtime) with alpha channel ?

No you can't upgrade professional license to broadcast license, So you need to buy new broadcast license if you need one.

We hope that aximmetry reconsider this topic.

I think you can record video with alpha using video recorder module and with mov file format.

For your first question Ahmed already gave the right answer above.

As for your second question, please read this topic: 
https://my.aximmetry.com/forum/postdetails/248-can-i-record-both-rgb-and-alpha-of-a-keye