You should be talking with your agent about both of these important issues since none of us here can possibly know what the material facts are.
In general, yes can you negotiate with the bank. Yes you can challenge their assessment of the home's value with examples of comparable sales and broker's price opinions of your own. The bank may not agree, but you can try.
I don't know if the encroachment issue is the deal-breaker that Ron is suggesting, but you need to talk with your agent about this as well. If you don't do some serious exporation regarding the potential liabilities of this before you agree to the sale in the first place you should consider thoroughly investigating it before your inspection and/or disclosure periods expire. Though I don't know the nature of the encroachment, it's hard for me to imagine that this won't involve talking to a real estate attorney in many cases. You may also think about holding off on spending money pursuing this sale until you really understand this issue.
Best of luck.