The same is true here in Oregon. The closing date is written as "on or before". If the lender can perform earlier and everyone agrees, you can close before that date. The only time, as an agent, that I feel concern is when closing dates keep getting extended beyond that original date. That generally means there is a hold up somewhere along the line either with financing or getting repairs completed. You, as the buyer or as a seller are never obligated to sign an extension. As a buyer, however, unless the home didn't appraise, you could lose your earnest money and for sure would lose home inspection and appraisal fees.
You can actually post ads on Zillow and then just "claim it" as the listing agent or the seller. Easy to do.
While an appraiser will certainly see that sale, appraisers go beyond just looking at a given area. I've had appraisers on many occasions actually call me about a listing or sale I was involved in to ask about overall condition and things like "seller concessions", in other words did the seller pay buyers closing costs. Many things have to be taken into consideration, not just proximity of the location.
My husband and I definitely recommend having your own website. Our local MLS only allows for 16 photos and with a home as large as yours, 16 just simply isn't enough to really showcase your home. Given most buyers start their search on-line before even speaking with a Realtor, you want to be found in as many places as possibly and when we do a webpage for a listing, we always have a professional photographer take the shots to really make your home shine.
While I've never seen anything in writing that can substantiate a health hazard, I always tell buyers to think not just about the purchase but what about re-sale down the road? It may not trouble you, but it may be a real turn off to others when the time comes to sell.
Not knowing your particular market I can only say that real estate is on the re-bound and you certainly don't want to offend a seller, if you are truly interested. Homes in my market area are selling for about 5% under list unless it's a short sale or bank owned.
I'd say "go for it". Here in my local area prices have increased by 4% this year and the market is re-bounding. Historically, my local MLS shows that kitchen and bathroom remodels are the most likely to see a full or nearly full return on the cost. Even if you don't recover all your costs, an attractive, updated home generally will sell faster too.
I generally make a request, if I'm representing the buyer, to set up a time just prior to closing to do a walk-thru and ask the sellers to take just a few minutes to go over things. If the seller is uncomfortable with that, then I request that they leave any manuals for appliances etc. on the kitchen counter. Most sellers are happy to do that but there is no requirement for them to do so.The anxious buyers....this isn't terribly uncommon. If security is a concern, I generally make certain to remove the lockbox once the appraisal is completed.