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1.They take readings every 30 second.

They don't  take readings every 30 second.

Do they take readings every 30 second?

Who take readings every 30 second?

They take readings every 30 second, don't they?

Do they or we take readings every 30 second?

2.The professor's assistant always shows us experiments in the laboratory.

The professor's assistant doesn't show us experiments in the laboratory.

Does the professor's assistant always show us experiments in the laboratory?

The professor's assistant always shows us experiments in the laboratory, doesn't he?

Who always shows us experiments in the laboratory?

Does the professor's assistant or the professor always show us experiments in the laboratory?

3.My friend goes (обратите внимание!!!) somewhere in summer.

My friend doesn't go  anywhere in summer.

Does my friend go anywhere in summer?

Does my friend go anywhere in summer or in winter?

Who goes  anywhere in summer?

They don`t take readings every 30 second/

Do they take readings every 30 second?

The professor`s assistant doesn`t show us experiments in the laboratory.

Does the professor`s assistant show them/us ( по грамматике можно подставить и тот и другой вариант, но более логично написать them) experiments in the laboratory. 

В 3 предложении у Вас допущена какая-то ошибка, поэтому там нет согласования. Я напишу два возможных варианта.

My friend doesn`t go somewhere in summer.

Does my friend go somewhere in summer?

это пишите если в предложении написано goes

или 

My friends don`t go somewhere in summer.

Do your/my (опять таки можно написать и то и то, но более логично your) friends go somewhere in summer?

Если в предложении написано friends