Can I use a new USB C dock with an old USB A socket? Can then the PD socket be used to supply more power to the dock?
The new dock will not damage your old USB A port. USB is backwards compatible, so connecting an USB 3 dock to a USB 2 (or older) system is not going to damage anything.

The old USB A plug does not support what is known as "Alternate Mode" in USB Type-C. Therefore you'll not be able to get the HDMI port on the dock working.

In theory, the USB related functionality such as the built-in 2 port USB hub, and the SD/TF-card reader will be able to function with your converter plug. However, if you connect it to a USB 2.0 computer, you will ofcourse not get USB 3.0 ports or speed on the dock. 

The type-C PD connector on the dock will not enable you to power the old MacBook Pro via the USB A plug, as it does not support the same type of power delivery as USB type-C.

Whether or not the hub in the dock gets powered by the way of the type-C PD plugin depends on how exactly that Novoo hub is designed. I don't think it is likely to work, as a 61W USB-C power adapter is working at 20V (~3A) - while the USB hub inside the dock is usually powered at 5V.