The transaction is now confirmed
Wow! Congratulations. You got pretty lucky there. I've seen similar transaction take weeks to confirm. Glad to hear that it worked out for you.
Are these transferred coins now free from that "dust" as they are now in different wallet?
Correct. It's the size of the outputs that matter. You had a few dozen outputs that were all less than 0.0001 BTC. You've combined them all into a single transaction that creates two new outputs. One of the new outputs is 0.1 BTC, the other is 0.00000304 BTC.
That 0.00000304 BTC output would still be considered small enough to be a problem, but I see that you included it in transaction:
https://blockchain.info/tx/9c6677c8cd63b28f3d7dc40ff0b6d0f6f018ffdff145723a8b959068d5ac3e67which combined a whole lot more tiny value outputs into a single new output of 0.20076942 BTC.
Yep, I did that, and for that new transaction I also used much bigger fee, as you advised, and that one went smoothly!
From now on, I will use different wallet for smaller transactions and I am also still downloading the whole block chain for the Bitcoin core.