The correct answers are 1. The weather is warm and sunny, and 2. My mother and I shop for warm clothes in winter
Step-by-step explanation:
As it is indicated in the chart for a sentence to be correct it requires the subject and verb to agree in number, which is known as subject-verb agreement. This means both the subject (agent of the action) and verb (action) need to be either plural or singular.
In the case of the sentence "The weather are warm and sunny" the subject "the weather" is singular, and therefore the verb form should be singular. According to this, it is completely correct to replace "are" by "is" which is the singular verb form of the verb to be. On the other hand, in "My mother and I shops for warm clothes in winter" the verb "shops" should be replaced by "shop" because "My mother and I" is a plural subject, and therefore it is incorrect to use "shops", which is singular.