Tanto mi madre como mi abuela escuchan la misma emisora cuando cocinan.

Here, tanto ... como means both ... and.

So:

• Tanto mi madre como mi abuela = both my mother and my grandmother

This structure is very common in Spanish when you want to connect two people, things, or ideas.

Compare:

• Mi madre y mi abuela = my mother and my grandmother
• Tanto mi madre como mi abuela = both my mother and my grandmother

The second version sounds a little more emphatic.

Because the subject is plural: mi madre + mi abuela.

Even though each noun is singular on its own, together they form a compound subject, so the verb must be plural:

• Tanto mi madre como mi abuela escuchan ...

A singular verb like escucha would be incorrect here.

Spanish often leaves out subject pronouns when they are not needed.

In English, you usually need they cook. In Spanish, the verb ending already shows who the subject is:

• cocinan = they cook

So cuando cocinan naturally means when they cook or whenever they cook.

You could say cuando ellas cocinan, but that usually sounds unnecessary unless you want extra emphasis or contrast.

Not necessarily.

Grammatically, cocinan refers back to the plural subject mi madre and mi abuela, so it means when they cook.

But in real usage, this can simply describe a general habit:

• both my mother and my grandmother listen to the same radio station when they cook

It does not have to mean they are physically cooking together in the same place at the same time. It can mean that each of them does this when cooking.

Because emisora is a feminine singular noun, so the article and adjective must agree with it.

• la = feminine singular definite article
• misma = feminine singular form of mismo

So:

• la misma emisora = the same station

Agreement is very important in Spanish:

• el mismo libro
• la misma emisora
• los mismos libros
• las mismas emisoras

In this sentence, emisora means radio station.

More literally, it can mean a broadcasting station, but with escuchan the most natural interpretation is radio station.

In Spain, emisora is a very normal word for this. So la misma emisora means they listen to the same station, not necessarily the same individual program.

Because escuchar usually means to listen to, while oír usually means to hear.

• escuchar = active listening
• oír = hearing/perceiving sound

With radio, music, podcasts, and similar things, Spanish very often uses escuchar:

• escuchar la radio
• escuchar una emisora
• escuchar música

So escuchan la misma emisora sounds very natural.

Because Spanish normally does not use the definite article before a family noun when there is already a possessive adjective like mi, tu, su, etc.

So you say:

• mi madre
• mi abuela
• mi hermano

Not:

• la mi madre
• la mi abuela

That would be wrong in standard modern Spanish.

Usually no. Here the present tense is most naturally understood as a habitual or general present.

So the sentence suggests a repeated action or normal habit:

• they listen to the same station when they cook

This is very common in Spanish. The present tense can describe habits just like in English:

• Leo por la noche = I read at night / I usually read at night
• Escuchan la misma emisora cuando cocinan = They listen to the same station when they cook

Yes, absolutely.

• Mi madre y mi abuela escuchan la misma emisora cuando cocinan.

This is simpler and also correct.

Using tanto ... como adds emphasis, something like both my mother and my grandmother. So the difference is mostly one of style and emphasis, not basic meaning.

Yes, but the meaning changes slightly.

• cuando cocinan = when / whenever they cook
• mientras cocinan = while they are cooking

In your sentence, cuando presents it as a general circumstance or habit.
If you used mientras, the focus would be more on the action happening during the time they are cooking.

Both can work, but cuando is very natural for a repeated habit like this.