can I update my old mac pro to modern standards?
That depends on the age of the Mac Pro , the budget and the time you're willing to spend.
If the Mac Pro is a MP 4,1 (2009) or newer it is possible. A MP3,1 (2008) can be upgraded to a modern level too, but is a bit more complicated.
Latest officially supported OS on the Mac Pro 4,1/5,1 : Mojave 6,1: Catalina
There are ways to install the latest OS too.
This is in a nutshell!
Could I then use the screen on my iMac as a monitor?
The iMacs between 2011 and 2014 support Target Display Mode.
If your iMac is 8 years old, that would be an iMac 2013.
Thunderbolt is the type of connection you'll need to use your iMac as a screen.
The only Mac Pro models that come stock with Thunderbolt ports are the Mac Pro 6,1 (2013) and the most recent 7,1 (2019).
BTW: another viable option is to upgrade your iMac replacing the HDD (fusion drive) by a faster SSD (~5X faster I/O speed).
Since Mojave a new disk format APFS was introduced which is optimized for SSD drives and doesnt really work well with HDD.
Some iMac models from 2013 came with an extra PCIe slot on the MainBoard where you could install a NVMe SSD ,which is ~ 30X faster than the stock HDD.
This upgrade implies removing the screen to open it, so should be done by a professional.
AFAIK max RAM is 32Gb (4x8GB) for a 27" model.