"no, no, my dear lady; i stick to my tea and bread and butter. it is much more wholesome in the long run—and a little more economical, too." what is peter implying when he speaks these lines?

He's implying that sticking to the basics is more better. A little more economical meaning he's saving money, while being better in the long run implies it is better for health than what the lady offered. Simplistically is sometimes the best.

The playwright wants the reader to understand that the main cause among the problems was the lack of communication and understanding among family members.

Explanation:

The excerpt presented in the question above is an excerpt from the play "A raisin in the sun" which features a family who received a large amount of money, which, despite changing their lives, proved that many problems affected all members of the family. These problems often become much bigger than what they should be due to the internal fights in the family, caused by the lack of communication, understanding and trust between the members. This is highlighted in the excerpt presented in the question above, where Walter, one of the main characters, feels uncomfortable with how the emotional distance between family members has affected everyone's lives.