If my original Windows 7 install DVD (not a copy of the original DVD) is left inside the DVD player on an infected machine, is it safe to use the DVD again? I am worried that the DVD has been infected by malicious applications.
In order to get any data to a DVD disk the DVD player must burn the data on it. If the disk is original it is normally read only.
If you have burned this disk yourself from the infected machine after it got infected it is POSSIBLE that the infection is present on the dvd.
Also some DVD images you can download from the less legal websites may contain some sort of infection (trojan, virus, spyware, ...)
So if the disk was burned before the infection or is an original disk it is safe.
No, a virus cannot do that.
The DVD is quite safe, a windows install DVD is a read only disk.
And even if it's was a DVD-RW (rewritable) the risk is very very very very small that anything could happen to it. It's theoretically possible to infect a DVD but I have never heard of it.
Its theoretically possible for a virus to flash a malicious update to the DVD drive, this has been seen once in the wild in 2011 and simply rendered the drive unable to read pressed disks.
This could possibly (maybe) infect an OS DVDR if the session wasn't closed in fhe form of a latent overwriting infection on some unimportant file such as an infrequently played WAV but as the ToC is fixed at the time of burning it would be impossible to change this to an active infection. A malicious program on an infected pendrive could then run the hidden code though.
In theory any flashable device is vulnerable even some network cards and monitors, malicious code can also be hidden in the unused area of the 24Cxx configuration memory on the flat panel and reinfect a cleaned machine...