Usb battery charging
This is not a simple matter. There are several types of charging ports in USB space. USB ports can support Battery Charging specification (which detects port charging capabilities via a special handshake on D+/D- wires). There is Apple-style charging "signature", using certain voltage levels on D+/D-. There is "chinese charger" signature, where D+ and D- are connected via a resistor less than 200 Ohms (the one you mentioned). Finally, there is a newer and insanely complicated "Power Delivery" specification. You need to decide which type(s) of chargers your device must support. If you choose several chargers, you device needs to solve a challenge of proper detection of all of them. Hint: this is usually done in sequential manner, and is not simple. One complexity comes when the port you are trying to connect to also tries to exhibit own intelligence to determine what kind of device you are. I don't think this problem has a solution.

And yes, there are plenty of charger ICs that can be configured to take whatever current you want in accord with optimal battery charging requirements. Brief look at Digi-Key shows about 400 ICs for charging single Li-Ion cell. Good luck to you.