Hi, the following is a website for a restaurant serving Jappa-jiru https://www.en-aomori.com/food-035.html
For the Stove train, you just go to the station that the train starts from and buy your ticket there. You can’t make any reservations. You’ll probably be getting on from Tsugaru Goshogawara station.
For the Nokke don, you go to Aomori gyosai center’s information desk and buy the coupon book. Then you go around buying whatever you want to put on your rice bowl with the coupons. http://nokkedon.jp/nokkedon/?no=2
You can look at this brochure of Hirosaki city to find something other than the castle to go see. I would go see the Neputa-mura. https://www.en-aomori.com/wp-content/themes/en-aomori/img/08_hirosakiguide_en.pdf