Type-C Non-Negotiated Power and 20V protection

This has been answered very well, but I will just add one point: You asked, "How much power do type-c power bricks provide if there is no CC negotiation and I just connect its 5V VBUS to my charging/PMIC*?"

The answer is zero. DFPs are not supposed to supply Vbus at all until they at least see some sort of pull-down resistance on one of the CCx pins. This is because, in principle, it's entirely possible to connect two DFPs together with a cable, and if both blindly threw 5V, the two power supplies might fight with each other to regulate the voltage.

With just 5.1 kΩ on each CCx pin, a UFP should expect to see 5V and only 5V as the other answers have said.

Type C can be messy, but the market is catching up to provide workable solutions.

Default Power

USB tries to be backward compatible, and the default behavior reflects this. Imagine that you're creating a wired adapter from Type C to a v2.0 Type A; if you just wire between VBUS and GND, you will be limited to 500mA.

But as I said, Type C gets messy. There are PD devices, such as the STUSB4500 or TPS65987 that provide advanced features for a couple dollars. This not only simplifies the design effort, but you also get support (and protection from liability) for any issues you encounter.

20V Protection

Best way to protect from from a surging input is to isolate from it, as the above PD controllers do; the STUSB4500 uses an external FET and the TPS65987 has internal switches that disconnect your circuit from USB until it is stabilized.

To me, this is keeping it simple; later you can decide to optimize for cost or size based on your experience in the market.

USB charging has become very complex but also very powerful. There are several official and de-facto standards used concurrently:

• USB 1.0 / 2.0 / 3.0
• Apple chargers
• Qualcomm Quick Charge 1.0 / 2.0 / 3.0 / 4.0
• USB Power Delivery

All standards will initially deliver 5V (or sometimes up to 5.2V to compensate for losses in the cable).

Plain old USB charger

The plain old USB charger will deliver 5V at up to 1A. Some chargers deliver up to 2A; usually they are labelled accordingly. They all disregard the USB specification (version 1.0 / 2.0 / 3.0), which specify 100mA / 500mA / 900mA.

Apple charger

Pre USB-C Apple chargers have a resistor between D+ and D- to indicate how much current the iPhone or iPad may draw. It's an unconventional approach as the communication usually works the other way round. They support up to 2A at 5V.

Qualcomm Quick Charge

Depending on the version of Quick Charge, the device and the charger can negotiate higher voltages. It always starts at 5V. If I'm not mistaken, you can draw 2A at 5V without negotiation.

USB Power Delivery

USB Power Delivery requires a compatible device, charger and cable. The device can ask for up to 20V at 5A (in 20mV and 50mA steps if PPS is implemented). The negotiation happens on the CC1/CC2 lines. USB PD will require a USB PD chip and a lot of software in device (about 50k of compiled code).

You most likely want to avoid USB PD as it's very complex. If you don't negotiate a voltage using USB PD, it will fall back to USB 2.0/3.0 behavior, i.e. you get 5V. But I'm unsure how much current you can draw. These chargers have power monitoring built-in and might cut your device off if it draws too much current (while older charger don't).

Summary

If 5V at 1A is sufficient, you shouldn't need to implement anything other than connecting GND and Vbus. If you need up to 2A at 5V, you might still get away without any additional logic for many chargers that offer QC or 2A ports. But it is likely problematic with USB PD chargers.

Implementing USB PD is a huge effort and most likely not worth it. As far as I can tell, there is no chip that implements it without the help of a MCU and a lot of code.

Overvoltage protection

I've implemented many USB solutions without overvoltage protection and never had any problems. I think it's only needed if your circuit is very sensitive. USB PD chargers have sophisticated power management and are unlikely to ever deliver higher voltages than negotiated. You should be more afraid of chargers implementing neither QC nor USB PD. They might deliver a short spike due to poor buck conversion regulation.