At what age does the child start understanding the difference between the spoken words which have different meanings but sound same?

Question

At what age does the child start understanding the difference between the spoken words like C, See, Eight, Ate, and Eat?

When I speak English, I find that my pronunciation is same for all the similar sounding words mentioned above.

I use "ate" when I am taking in past tense. I do pronounce eat and ate differently. But, the child uses "eat" to say whatever she wants. Example she says (after putting the pen in frog toy's mouth): "Frog eat pen". Whereas it should be Frog ate pen.

Child is currently 2 years old.

Answer 1

According to the abstract of this study of 60 3-year-old children:

From these experiments we conclude that children have the metalinguistic skills necessary to identify homonym pairs; moreover, they realized that homonyms represent two different categories. Finally, if children have a one-to-one mapping assumption, it is not strong enough to prevent them from acquiring homonyms.

However, this study involving adults and children found that younger children (grades 5 and below), will make fewer context-based interpretations of homonyms than adults.

The results suggest that homonymity is a powerful inhibitor of children's tendency to derive a meaning for a new word from context.

In plain terms, that means when a new word which sounds exactly the same as an old word (is a homonym), children have difficulty ascertaining the meaning of the new word from context.

The author of this last study, Michèle M. M. Mazzocco, has also done other studies regarding homonyms that may be of interest.

While this question asks about toddlers, research involving homonyms and homophones often includes older children. This study specifically studied 9-, 10-, and 12-year-olds and found differences.

Another study found that in children 3-6 years old, the ability to understand the homonyms grew with age, with a jump in ability around 4 years old.

This appears to be a subject that has ongoing research being done, with no clear, conclusive age about when homonyms are best understood. I would arrive at the interpretation that homonym acquisition is an ongoing process, rather than one that "turns on" at any given age, and that process can be helped along by reinforcement from parents and educators by using the homonyms in clearly different contexts. To use an example from one of the linked studies:

"The people are dancing at the ball."
"The players are hitting the ball with a bat."

Provide two clearly separate contexts for the homophones. Whereas

"They threw a ball."

Is potentially unclear, as it could refer to either of the homonyms.

Answer 2

I have found that it comes along as I have corrected my daughter's speech over the years as well. At the age of two I'd say she's doing just fine.

According to this chart, she should be barely understandable. Sounds like your child's speech is on track, although it doesn't cover when you get into present versus past tense.

According to this site, your child is on the brink of tremendous growth in their language abilities. This stage of development is when word knowledge leaps from around 50 words or so up to 200. These are just different words, not even covering the tense of the words.

I would say, similar to what @DanBeale said in his comment, to keep talking with the child and model good language habits.

Edit

I realized I didn't actually answer your question of

At what age does the child start understanding the difference between the spoken words like C, See, Eight, Ate, and Eat?

I can't seem to track anything down regarding the answer to that exact question. Some of it may boil down to when they learn the word. You can help differentiate between the two by comparing them. "Letter C looks like this. I see the letters."