Dell Inspiron 7570 Type-C

The C or 3.1 port will not charge your laptop.  Its for charging phones or other small low power 5VDC (USB Power) devices that can be charged.  

Connecting a USB 2.0 device to a higher speed port, such as the 3.1, will not increase speed.  It will still be at the USB 2.0 device speed.    

@taabi, for the first question, it's not entirely clear because the spec just says "Power Delivery".  The reason that's a problem is that USB Power Delivery can send power in either direction.  USB PD can be used for the system to provide additional wattage to peripherals that support USB PD (typically either 7.5W or 15W), and/or to receive power to charge the system itself.  Some systems support only the former, some support both, and I suppose some might only support the latter.  Dell sometimes clears this up in their specs by specifically mentioning "system charging" or "DC in" for the USB-C port to confirm charging support, but I've seen reports of people successfully charging systems that only showed "Power Delivery" in their specs like yours.  I know it's frustrating not to have clearer information from the specs.

As for the Type A to Type C cable, those are used to connect a USB-C device to a USB-A port, not the other way around.  One common use of these cables is to charge smartphones that have Type-C ports from "regular USB" power sources.  You would need a Type B to Type C cable to connect a "regular USB" peripheral to a Type-C port, since USB-A is the port found on host devices (like PCs), while USB-B is the port type found on peripheral devices.  But regardless, the device will only perform up to the maximum USB spec that it supports.  So if it supports only USB 3.1 Gen 1 (or USB 2.0), it won't perform at USB 3.1 Gen 2 speeds just because you connect it to a USB-C port that supports it.  Also be aware that there are a huge variety of USB-C cables, including USB-C to USB-A cables.  Some of them only support carrying USB 2.0 data, for example.  So if you use a cable like that, you can actually bottleneck your device.  For USB-C to USB-C cables, versions that only support USB 2.0 are typically used when the cable will be used primarily for charging devices from a wall charger, for example.  The more common setup is cables that support USB 3.1 Gen 1, which means it would also support video output.  Cables that support USB 3.1 Gen 2 are also available, but they're more expensive and currently are only available up to 3 feet long, and I don't think I've ever seen a C to A cable that supports 3.1 Gen 2.  But USB-A ports that support 3.1 Gen 2 are very rare anyway.  I wrote a detailed post about the ways that USB-C cables can vary in specs here if you're curious.

Nope,you are wrong about charging. The dell 7570 supports PD 2.0 . It even gets PD- firmware Updates. One can charge this laptop with 65watt type c charger.

Yes, the DELL 7570 Supports Power Delivery. It charges perfectly from type c port. You can use any 65 watt PD Adapter. More  Over it supports Display Out as well as 5Gbps data transfer rate from this Type c Port.