Can we bring these food over to Japan?

My mom wants to make porridge from them to eat as she can't eat wrong food. Its been 6 years since we last went on a family trip.

1. I want to ask if its okay to bring these to Japan in checked luggage.
2. Are there any white bread without egg available in Japan to buy? If yes, we can strike that off the list.

We need rice too but we decided to buy over in Japan. As its quite pricey in Japan we want to try to bring as much food from home as possible. I know Japan is strict about importing meat products so we won't be bringing that, just canned tuna.

Please help, Thank you.

Red dates
Wolfberry
Ginger
Carrots
Barley (solids)
Protein powder
Ensure milk powder
Canned Tuna
White Bread

Description:
http://www.maff.go.jp/pps/j/introduction/english.html

Database where you can do a search for individual plant:
http://www.pps.go.jp/eximlist/Pages/exp/conditionE.xhtml

Very doubtful most of those would be allowed in. Not just Japan but worldwide.

Meat and diary is normally a no no.

Plants grown under ground again are normally a no no.

Anything out of commercial packing is a no no.

The canned Tuna is about the only on I would say for certain is allowed.

Check the about website link to for further information.

Produce generally isn't allowed when crossing international borders, so carrots are going to be a no-go.

I'm guessing this is your first trip to Japan, and you may have been misinformed about the local price of foodstuffs, because bringing your own vegetables is unlikely to save you a significant amount of money. It's not like carrots are at all rare or prohibitively expensive in Japan. They're one of the most commonly eaten vegetables, showing up in salads and curries even at extremely cheap restaurants.

More importantly, how long can you keep carrots before they go bad? Maybe a week? So you're not going to be able to bring more than a week's supply with you.

And how many carrots are you planning to eat in that week? Two dozen? You could go to a supermarket in Japan and easily buy two dozen carrots for less than 2,000 yen. Heck, here's the online order service for one of the Tokyo area's most common supermarket chains, and they're selling them for 68 yen each.

So you're going to try to haul two dozen carrots in your luggage to save, what, about 1,600 yen, minus whatever you paid for them in your home country? Would saving 10 bucks really be worth that hassle, even if customs did allow you to bring raw vegetables into the country?

^^^ This

For white bread without egg , you can check link:
卵不使用食パン (Tamago fu shiyō shokupan)
Japanese site , author has a child with egg allergy. List of bread/links on the web.
https://bit.ly/2Le6Qmf

As for other stuff, unless it is processed and packed commercially food, chances of bringing it legally is slim. The Chinese herb stuff, milk/protein powder you may get away with it.

Have a look at this video clip about foodstuff prices at supermarket. Prices might vary (not much) depends on location/season. Will give you a rough idea.
https://www.youtube.com/watch?v=GhNbH7g3b6g

It would help if you can point us to which city/region you'll be visiting, then someone can/may recommend how/where to get some stuff.

Okay thank you guys for your responses! I appreciate them a lot!

thank you for posting and sharing useful information