Which phrase is correct between "in this sentence" and "on this sentence"?
Examples:
1. Our teacher dilated on this sentence structure in class.
2. Indulge me on this next sentence.
3. What does the word mean in this sentence?
4. There are no mistakes in this sentence.

Or "in" and "on" are exchangeable to indicate a sentence?

Question

Which phrase is correct between "in this sentence" and "on this sentence"?
Examples:
1. Our teacher dilated on this sentence structure in class. 
2. Indulge me on this next sentence. 
3. What does the word mean in this sentence? 
4. There are no mistakes in this sentence.

Or "in" and "on" are exchangeable to indicate a sentence?

Answer

1. Our teacher dilated on this sentence structure in class. ('Dilate' is the wrong word to use in this sentence. See http://learnersdictionary.com/definition/dilate)

Sentences 2, 3, and 4 our correct. These examples do not use the words 'in' and 'on' as prepositions of place, rather these are preposition-verb collocations.  How we know whether to use 'in' or 'on' depends upon the verb they follow.  Unfortunately, for language learners, this usually means memorizing lists.  Here's a good one for you to use:  http://eslgold.com/grammar/verb_preposition_collocations/

Answer

Hi Salvater;
They are not interchangeable.  "On" refers to the entire sentence.  "In" refers to a single word, clause or phrase within the sentence.  "With" could be used interchangeably.  I hope this helps.
Thanks,
Stephen