I wouldn't accept an offer less than appraised value, but it is a good jumping off point for negotiations.

As far as the junk in the yard, talk to the RE and tell him you would add $X to the buying price for it to remain. You will need to be really sure of exactly what is there and exactly what you want left behind though. Last thing you need is to have her leave whole heap of useless **** everywhere, or a pile of asbestos hidden in a car body......

Good luck!