As the others say, a homeowner's warranty is a good marketing tool. It's not a red flag; it's more like a green light.
As for flooring, you've gotten a wide range of opinions on that. First, if the expectations/customs in Downingtown are clearly on one side or the other (and your Realtor can advise you if that's the case), go with that. However, let's step back a minute and analyze the situation.
If you do nothing--leave the worn carpet in place--let's assume you get 10 people looking at your home. These numbers aren't exact, but in many cases it'll be something like: 5 people take a look; their reaction is "shabby house, ratty carpeting, let's move on." 2 people take a look: their reaction is "We'll have to put in new flooring. It may cost $10,000. We can't afford that. Let's move on." 2 people take a look: their reaction is: "We'll have to put in new flooring. It may cost $10,000. So let's make an offer, but let's make it $10,000 less than if the flooring were good." And 1 person takes a look and says, "Good potential. Let's ask for a $3,000 allowance. Or let's reduce our offer by $3,000."
So AT MOST 1 or 2 out of 10 would even consider consider making a reasonable offer if the rest of your house is OK and meets their needs. The others won't make any offer, or they'll overestimate the expense of the flooring. (Happens all the time.)
Now consider the alternative. You put in $2,000 worth of carpeting, or $3,000 worth of wood floors. Your home price is the same; you're just not offering the allowance for flooring. You get those same 10 prospects through your house. They're all looking for precisely your type of house in your price range.
5 out of the 10 don't even notice the flooring. It's fine. It's good. 3 out of 10 love it. They love the new wood and the fresh carpeting. 1 hates it. They love green shag carpeting, and you went and put down a nice neutral pile carpeting. And 1 was looking for a bargain, a fixer-upper. But now you've gone and put some money into the property, so now their low offer is less likely to be considered.
In this scenario, if those 10 are looking for your type of house in your price range, and the rest of the house is good, the new flooring is a positive to 8 of those 10. It's only a turn-off or a negative to 2 out of those 10.
So, which works better for you: 8 out of 10 being turned off, not making an offer at all or making an unreasonably low offer because of ratty carpeting? Or only 2 out of 10 being turned off because you replaced the ratty carpeting with nice, new carpeting or even wood?
Replace the carpeting.