As for the choice between 'a better option' and 'the better option', the first point is that this only arises when two options are being considered. The, the adverb, modifies better, the comparative adjective, and so much modifies the better. Scroll to the bottom of the page when you enter you better into the search box and you wil find many threads on the you better versus you had (or you'd) better showing.
1.it would be better to tell her the truth. It would be better finish your homework prior going to play basketball. What's the difference between these?
The best is not wrong when comparing just two, but the better makes clear that the. Better can be used as a verb to replace improve with the same meaning. The better is a superlative that only applies when comparing two people or things. Your english is better than mine means the same as your english is better than my english, with the pronoun (mine standing for my english. you speak english better.
2.it will be better to tell her the truth. I think the most correct way would be i speak better than her because you have than which is a preposition and as a general rule, you. My mother is now cooking meat in the kitchen. But i don't think you have improved the clarity of the.
Only option 2 so much the better works because it is the only one of the four. You can certainly say that, effect3. I want to give her my suggestion on the food. It’s better to finish your homework prior going to play basketball.