"After a few days, eBay started nagging me to update my listing and lower the price. Then, they enabled the Make an Offer option without my enabling it."
^^^I have never heard of that happening^^^ There is a an automatic lowering the price option that may be check and you need to uncheck it. I have sold a fair amount of items on eBay and that is definitely and option that you can choose. I have never had eBay purposely change it. I currently have 15 or 20 items for sale.
As far as making an offer, it works both ways. As a seller, I have my "Make an Offer" items set to automatically accept an offer defined as a certain amount, and automatically reject an offer if it is way too low. I recently "sold" a 16 port Ethernet switch. I had it listed for $185. The guy made an offer, which my automatic settings accepted. A day went by with no payment. Two days, then three then four days without payment. I don't get too excited about stuff but I sent him a message about non payment, including an invoice. His response was that he was trying to pay but couldn't because there was a glitch and PayPal wouldn't take his money (yeah right). Finally, after 8 or so days I filed a non-payment complaint with eBay so at least I could get my sellers fees refunded. Yes, we get charged sellers fees if the item sells but the buyer doesn't pay. He sent me another BS message about he couldn't get PayPal to take his money. He then asked me if I had relisted it, which I had and forwarded the item ID to him. My guess is he thought he could shoot a low offer and I wouldn't take it. When my settings took it, he was probably going "oh crap, I don't have the money for that".
Another dude made an offer for a Trumpf laser part that I have. I am about 99% sure he is from India. I don't ship to India. He sent me some crap message about he will take it if it is good shape or new, blah blah. Like he is doing me a favor by taking it off my hands. I ignored him. Later, I get another offer from a different eBay user, but I think it was actually the same guy. My gut told me it was the same dude. Ship to Poland now. Both eBay users had 0 for a feedback score and both had just signed up for an eBay account.
So, as an eBay seller, there are quite a few scammers out there, and it seems to be getting worse. I have never had an eBay purchase go bad on me yet though.