the word shall and will be
Tommorrow, I shall buy some vegetable from the market. why cannot use Tommorrow, I will be buy some vegetable from the market.

Question

Answer

shall 是過時的英語。太文了。

你可以說
Tomorrow, I shall buy some vegetableS from the market.    
OR
 Tomorrow, I WILL BUY some vegetableS from the market.

口語從未說shall

Answer

You can say "I will", but it is a different expression.

You say "I will":
1. When you make up your mind on the spot. E.g. I'll get some vegetables then.
2. When you are waiting to make up you mind. E.g. If it rains tomorrow I won't go.

The example phrases you have given are kind of dead, as they don't really mean anything when not in context.

Answer

shall= you think it would be good to buy vegs tomorrow
will=you are going to buy them tomorow for sure