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Does making your BOT play with higher rated opponents make it stronger

No it does not and it is useless as it can be defeated by stockfish5
If you're looking for how to create a BOT account and select an engine of your choice, I would go there: github.com/ShailChoksi/lichess-bot (This requires you to be familiar with the Python language).
If you're actually looking to code your own chess engine from A to Z, this is the site you should check: www.chessprogramming.org/Main_Page . You'll find everything you need documented, from the search function to the evaluation heuristic and the communication protocols.

Either way, good luck :-)

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