Has the bedbug problem with Turkish Airline flights been resolved?

No, the "issue" has certainly not been resolved, and probably never will be.

The "issue" is that there is an endless firehose of disinformation, nonsense and outright lies posted all over the IBM (Internet Bullchit Machine) with so-called "first-hand reports" of various infestations everywhere. Many people actually believe any lie they see posted on a screen. The result is...well, look around you.

"Fuel charges" - where are you seeing that? That sounds like an old fee added to award tickets (paid for with frequent flyer miles) - sometimes referred to obliquely as "YQ". What kind of ticket are you looking at? Assuming you are buying your ticket with money, you can ignore whatever tiny details may be listed as to what components (taxes, fees, surcharges, etc.) make up the price of your ticket, and just look at what they're going to charge you. Is the bottom-line price OK for you or not? (as you say, alternative flights are twice expensive, so who cares what the fuel costs, compare the all-in ticket cost). It shouldn't really matter what price ingredients are baked-in (there is typically a long list of things that go into any airline ticket price, and few of them can be controlled unless you go somewhere else).

FWIW, I fly Turkish Airlines pretty often (once or twice a year in recent years). I think it's a great airline and I actually go out of my way (literally) to fly with them. For me, they tick all the good boxes. No bugs, no snakes, no rats, no kidding, but yes with comfy seats, decent food, modern new planes, good and sometimes great service. One of my favorite airlines. YMMV, but there are lots of TK fans here and elsewhere. By some measures they are the world's largest airline, with flights to more destinations than any other. They must be doing something right.

Also, is fuel charge ($400) normal (economy)?

A lot of European airlines call part of their price a “fuel surcharge”. U.S. airlines aren’t allowed to call something a “fuel surcharge” so the cost of fuel is just built into the base price. Unless you are booking with frequent flyer miles (where you pay taxes and surcharges), the only thing that really matters is the total price.

Some very clear air in Seattle today. Enough to blow the IBM rumours clear across to Idaho.

@Laura-Could be. I thought it was a big “fee” added to the list price. I don’t recall I’ve seen other European airlines assess this quite big fee, IMO. Admittedly, I don’t travel with European airlines often and my memory could be fuzzy.

@David-No I am not booking the flights with miles. I was surprised at the large difference between the list price and the final price so I checked the breakdown. I don't disagree with you what matters is the final price but I found the list price a little misleading-or maybe it's just I am not used to this kind of pricing.

I did a test: I tried to book the flight with a third party and the final price didn't include the fuel charge. Strange... I won't book the flight with a third party though.

@ jeansn6 - It's not clear (to me at least) where exactly you are seeing the pricing details. If, as I think you said, the price you are looking at is half what other alternatives charge, and that's the price you're (potentially) going to pay, then whatever details they may or may not show as how the charges break down, then I would not have any concerns.

If they're advertising or showing an attractive price (half of what the alternative would be), and there's no last-minute trickery going on with adding a so-called "fuel surcharge" on top of that, then to me the internal pricing details are just noise which can be ignored.

Of course, check to be sure you are doing apples-to-apples comparisons (what is/isn't included - things like checked bag, choosing a seat, meals, etc.) and you make your choices about how important (or not) those details are...all that said, I think many people are pleasantly surprised (even delighted) at their Turkish Airlines experience. If you're thinking of it as some sort of sketchy "developing world" low-end airline, it is nothing like that. They win awards regularly as the (or one of the ) best airlines in Europe (although with many Turkish things, how European and how Asian they are may be in the eye of the beholder). Now, they're not perfect (I have run into quirks and annoyances) but no airline is perfect. I'm generally quite happy flying them.

If you get out the magnifying glass and the green eyeshades to look carefully at any airline's pricing details, there are lots of details that may not make much sense. If you see some part of your ticket cost broken out as "fuel surcharge" (or "payoff to some oligarch") I wouldn't lose much sleep over that, it's just the cost of doing business. Of course, if they smack you with an extra $400 on top of the price as soon as you pull out your credit card, well that's another story.

In any case, it's a good airline IMHO. If the price (the price you pay) works for you, and other details that matter to you are in your comfort zone, don't let the "exotic" nature of the airline worry you. They're fine (and IME better than most). Hope that helps.

Just did a trial booking on Turkish site, economy class, and got to the payment page and saw no 'fuel (sur)charge' fee.

What site are you using that displays/adds a fuel fee?

@joe32F-You have to go thru all the steps until you reach "Payment". There, at the bottom of the page, below all those payment options, if you click on the Price, you will see the details: Base Fare, Fuel Surcharge, Taxes and Fees.
I know what matters is the final price, but I also want to know what make up of the final price, i.e., how the price goes from the listed to the final. It's fine other people don't care.

I hope that you are using the genuine official app or website, not a lookalike ....

happy travels

I did another trial and i think earlier I somehow got the list price wrong (I don' know why and how though). Anyway, the bottom line is that it appeared that the Fuel Surcharge is included in the list price. And you can see the breakdown of the final price (Base, Fuel, Taxes & Fees) when you reach the Payment page.
My apology for the misunderstanding on my part.

@Nigel-I was using Turkish Airline's website, I am certain about that. Thank you for the reminder though.

For me, they tick all the good boxes

David!!! TURKISH AIR HAS TICKS ON BOXES!???

I don’t recall I’ve seen other European airlines assess this quite big fee,

Here is an article that shows some of the airlines that have this fuel surcharge.

https://upgradedpoints.com/travel/airlines/airline-fuel-surcharges/

I'm not really sure what thr point is? If you don't like their price, fly someone else. Not like they are being deceptive. You get to choose.