I'm not sure how that works? you connect the pi to your laptop and use putty to login?
This would also require one of those tty-to-usb cables?
No, just a regular USB cable. USB's CDC protocol makes it look like a serial port to the host PC.
Or even better USB OTG.
You can do this with gadget mode, the g_serial module.
Sure, but it has two USB sockets of which one is only used for power supply; if that one could also be used as OTG (instead of just TTL RX/TX as suggested by the fellow) that would be great.