According to the website the tickets don’t go an sale until February 27 so you might be a little early. Additionally I have reached out to my son in Kobe to see if there are alternative outlets. When I hear back I will post his response.

They check bags but are pretty relaxed. I was able to bring a backpack and my metal water flask.

The people sitting next to us had small snacks, don’t know if they snuck it in. But you’ve got to buy sake from the vender- where else in the world do you have that opportunity while watching baseball:) the locals offered to buy ours. Gotta love Japan.

When I was there people seemed to bring anything including lunchboxes.

We bought our tickets several weeks in advance, so I am unable to answer you question regarding tickets at gate. We went to the game on a week day and the ball park appeared to be full. I did not notice a lot of empty seats. If you can buy the tickets in advance, I would recommend it. If you are already in Japan, the people at the front desk of your hotel can help you. A Japanese travel agent can also assist you. Yes, you can take a back pack into the ballpark. People were carrying bags with noise makers and food. We sat in the outfield and had a experience of a lifetime. Please enjoy the game and the atmosphere. Regards