I brought 3 tonnes of stuff from Nepal to Istanbul about 18 months ago - basically 10 years' of household effects from 2 houses plus a lot of electrical stuff (digital speakers, instruments) and small furniture.
Second part of your question is more tricky, as I didn't personally handle their rescue from customs. If I had gone in person, probably would have cost more limbs than I have, so my ex did it. (Mostly her stuff anyway.)
I don't have much recollection, but things that come to mind are that she had to do a lot of smiling and waiting, open every box (more or less), explain how some of the more valuable items were worthless and only of sentimental value, etc., etc. I also recall that she couldn't actually remove the stuff, but had to hire a company based at the airport (SAW) to do the transportation (though they were regular priced), but you may be able to arrange for Yurt Ici Kargo to do the pick up / transport.
They must have been feeling generous, or were convinced that a poor person mad enough to import tonnes of rubbish (and there were dumbells in there, folks, as well as, believe it or not, one plastic bag full of trash), as we got away with about 200 $ for import duty on 1 or 2 items and about 500 $ to drag the whole lot down to Bodrum. Amazingly all things arrived safely.
There was a form to fill out. Sorry for being so vague.
To be more practical, I would talk to a cargo company in Dalyan about it. Take along the manifest which should list each item box by box / value by value and ask them to do the processing - my guess is it would be a flat fee for the releasing your stuff from customs, a by volume/weight fee for the transport and whatever duty they hit you with.
Only try to do it yourself if your Turkish is good, your patience is limitless and you can do a good church mouse impression. I am sure someone in Dalyan in this forum can give you a recommendation ...
good point ... my stuff turned up on the same flight as me (by coincidence) ... customs people said it's better to bring it as baggage and they can waive it through, or will inspect a bit and accept a token declaration (couple of taxable things) to save them the hassle of storing, inspecting and releasing ...
The basic rules are airfreight or cargo has to go through customs at Istanbul or Izmir, allegedly Dalaman does not have the facilities!!! If you use someone like DHL they will take care of it all and deliver to your door, well I say that, the dhl agent locally is Aras cargo in Ortaca and they have never been able to find my house, I always have to go and collect it but I am sure a big amount they would deliver!
If you fly BA you can increase the number of bags, each with a 23 kilo allowance, upto a maximum of 10. Last year I think it was 28 quid per extra bag. I moved all my things this way as it was the cheapest and easiest option - including a vacuum cleaner and 19" TV. It's an easy drive to Dalyan from Izmir, or you could catch the bus and send the bags cargo.
Having been in an export business I had good contacts & we sent 35 boxes of personnel effects direct to Dalaman by air, it was 5 1/2 years ago so can't comment on today. Yes, they opened all the boxes but it only took a couple of hours & we paid £80 duty, plus we took our own pickup at a cost of around 30tl. I do think it's essential to have an accurate inventory for each box & we had to have it professionally packed for the insurance. Do you still have to have residency to pick up from Izmir? we did'nt know this & did'nt have it when ours came.