1. ChipMixer does not seem to provide any mixer code to track the BTC sent to an address. So, is it possible to get back BTC from the same address, in a subsequent mixing?
You can't, because outputs are faster than inputs from a blockchain perspective; you can't receive chips which were created using your just deposited funds, because you can only receive chips which were made before your deposit.
Actually, you can. The next time you use ChipMixer, it is possible you receive chips that were (partially) created from your own previous deposit. But it doesn't matter, you can prove (with a signed receipt) that those coins came from ChipMixer:
What is a signed receipt?
Our goal is to make Bitcoin value independent of its blockchain history. Some governments and corporations wants to invalidate its value by claiming they are connected to something immoral like gambling. Every time you withdraw from ChipMixer, we give you cryptographically signed receipt that proves you have received those funds from us. Since the disconnection of history is proven, there can be no loss of value.