Mount PC's HDD on Mac, with a USB from Mac to PC

In short, no.

USB needs a 'master' at one end & a 'slave' at the other. You cannot connect two computers that way - each expects to be 'master'.

You'd be far better off putting the drive in a USB enclosure then connecting that to the Mac.

NTFS write can be either enabled natively or using 3rd party software - How do I write to NTFS drives in OS X?

You can transfer files over WiFi or BlueTooth. For fast speeds you can plug both computers into a router via Ethernet cables and communicate over the network that way. These are the non-invasive approaches that don't require special cables or enclosures for the HDD you are copying from. You can also try a file sharing server like Samba that you run on one machine and use the other to transfer from. You won't need special drivers for NTFS if using one of these networked approaches.