Yes, they will need to get a "Correction Deed" filed of record to correct the issue.
Yes, you can sell your home as-is. Selling as-is hinders a purchaser's ability to sue you unless they can prove you committed fraud. I always sell my personal properties as-is to limit my company's liability post-sale. Can a purchaser sue you. Sure they can. It only takes a few hundred bucks and a desire to make your life miserable to file suit. Will the plaintiff prevail? It's much less likely if you include as-is language in your contract and deed.
No, there is not Texas law that requires any such thing. If you're referencing Federal income tax rules under the IRC, that's a different matter. However, there are exemptions if you've lived in the home in two of the prior five years.
Generally speaking, yes. But you would have to factor in other variables such as cost / benefit and overall market conditions. If homes in your area are selling fast and at or very near asking price, taking on the expense of staging may not be necessary.
Clearly many buyers will not consider such a home under any circumstances while others will overlook the issue if the home is in better condition and is properly staged to establish functionality. Just look at homes backing to other major thoroughfares such at Parmer Lane up north and Hwy. 290 out west. These homes still sell when precautions are taken into account initially. Don't assume you will take a financial hit until you've gotten all the information to prove that assumption.
Keep in mind that there is not enough information in your post to provide guidance on what you're seeking. Style of home is good start, but what about price ($200K? $800K?), location (Killeen? New Braunfels?), size (1,000 s.f.? 5,000 s.f.?), etc. Also, you may want to define "reasonably priced" since this has very different meanings to folks. Do you mean reasonably priced retail or a reasonably priced investment grade property.If you're seeking investment grade, those deals will seldom hit the market. They'll typically be sold by investors to investors without the assistance or involvement of a brokerage.
Texas is a non-disclosure state, meaning we don't report real property sale prices publicly. As such, any online value estimates will be very rough estimates at best. Trust the appraisals.
If the listing agent refused to show you the home and he knows you're not represented, he has almost certainly violated the Code of Ethics and his fiduciary duties if you are a qualified buyer.
You need to refer to the terms of the purchase contract, if any.
The reason for the substantial upfront investment the builder requires is so IF you do walk away, the builder doesn't suffer any harm. My guess is you will not see this money again regardless of what the contract stipulates.