Can I use my iMac 27 (2009) as a second monitor for my iPad Pro 12.9 v2

iPad doesn’t support mirroring to a Mac or PC, but recent Mac computers with MacOS Catalina can use iPad as an extended display using Sidecar:

https://support.apple.com/en-gb/HT210380#systemrequirements

An alternative to Sidecar is Duet - but again this provides an extended desktop from Mac to iPad:

https://www.duetdisplay.com/

Yes. Most models of iPad are able to output to HDMI using a suitable Adapter (you’ll find Apple HDMI Adapters for both Lightning and USB-C models of iPad - in addition to third-party options). USB-C equipped models also support DisplayPort over USB; additionally, the 2021 “M1” models of iPad Pro support connection to Thunderbolt displays.