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Where you stuck in this?
I use MCP73832 Single Cell Li-Ion Li-Po Charger Controller, its cheap and easy, and works like charm.
Your IC purpose is little different and according to datasheet you should use resistor on pin 2 ILI_SET to set current limit. External resistor used to set current-limiting threshold, recommended 16.9 kΩ ≤ RILIM_SET ≤ 750 kΩ.
On USB 2.0 max 0,5A on USB 3.0 max 0,9A see page 11.
TPS2511 datasheet
https://www.ti.com/lit/ds/symlink/tps2511.pdf
If i follow the sample circuit, can i design it for up to 1.5A to work as a DCP ?
Yes according to datasheet, but not on USB 2.0.
Yes that is true, and its ok if you have free additional USB ports, and you want to use and carry cables with few USB connectors. I saw USB cables with two connectors, but not with three or more.