Gift Tax Strategies on Property from Mother-in-law

Burner for sensitive stuff.

My spouse's mother would like to gift us her manshon.

Renovated units in the same building are generally listed for 2200-2900man so it is probably safe to say the maximum value would be no more than 2900 man.

Per this https://www.nta.go.jp/taxes/shiraberu/taxanswer/zoyo/4408.htm, if my wife were to take sole ownership and IF the assessed value is 2900 man, it appears the tax would be

(2900man – 265 man) x 45%

Assuming the above is right, my questions are

1. Father-in-law committed suicide in the unit about a decade ago. I understand this affects liquidity but does it affect assessed value for gift tax?

2. If she sells to us below assessed value, am I right to assume the difference between sale price and assessed value is considered a gift? Or is it just fraud?

3. Is there a better way than #2 above (other than obviously sale at assessed value) that allows the money to go to her instead of to taxes?

4. If the answer to #3 is "no", is there a more tax efficient way to transfer ownership (e.g., split with me or spouse's siblings)?

u/sendaiben, I've seen you mention you may also takeover the in-laws' home. Have you looked into the taxes at all?

Thanks any and all in advance.