Hi Refael Shamir,
1. You are correct, Not all of Type-C port support Power delivery by default. This is because the designer think 5V power voltage is enough for the design. So, they could only support Type-C SPEC.
2. If you could like to make your device detect as a DFP (equal to power source), you should pull-up 56K from CC to 5V.
3. You do not need an "active" cable for negotiating such power drawing via the USB-C.