I consider the budget realistic. No one here agreed to fixed prices, but the cost estimates were all very realistic, and the actual price was even slightly below the estimated price several times.
For 50,000 below the offer, you can completely forget it here; rather, you have to add a lot. But if the house has been on the market for 3 months, it’s worth a try, even though I would have offered at most 20,000 less. Communication helps. Deducting the renovation costs from the offer price would never work here because the price is normally already adjusted to the condition.