2) By getting direct transfer, you as the owner already saved up a big amount of cost. You no need pay stamp duty and you no need pay legal fees to transfer the title to your name. You can skip this process since developer allow to direct transfer to the new buyer.
So in my opinion, all costing, admin fees, penalty etc charges by the developer in order to skip the transfer title to your name first, you should be the one bearing.
If charged on the new buyer, must as well the buyer go buy from other owner that got their title done and perfected.

3) Stamp duty for you is based on your original S&P price.
Stamp duty for the new buyer is based on the selling S&P price.
You and the new buyer pay separately, is unrelated to one another, that if the developer disallow direct transfer, therefore you need to transfer the title to your name first, then only able to sell. But seems like that is not the case so this question is not relevant.