So, we went to a beer garden with our friend's to celebrate his birthday.

We had prepared a birthday plate to suprprise him without telling him.

English = perfect.

But a birthday plate is not an expression we use.

Do you mean cake? present?

If you truly mean plate then you would need to write;

"We had prepared a special plate for his birthday to surprise him without telling him."

Also

Surprise means not telling him --> so --> "We had prepared a special plate for his birthday to surprise him" -- or -- ""We had prepared a special plate for his birthday without telling him"

It looked like he was verry happy when my other friend brought the plate, but at the same time, I was also suprprised because my name was also written on the plate like " Happy Birthday Shinpei(my friend's name) and Kazu(my name)".

Actually, it's my birthday on June 29th, so my they had also prepared it for me without me knowing.