If I had a firewall with two interfaces - one to an internal private network and the other on a link local network (169.254.0.0) - and sent all questionable requests to the link local computer, could a virus on that computer get access to the private network?
A virus is just a computer program. If
Computer A can communicate with
Computer B by any means, a virus on
Computer A can reach
Computer B. Reach, not necessarily infect.
To a virus infect
Computer B, it must use a vulnerability, usually remote code execution. On a network where all computers share the same OS version and the same group of applications, usually infecting one computer via network is enough to infect all others.
If the firewall allows traffic from link local to the other network, any virus on
Computer A have the possibility of reaching
By definition, a link local IP address should not be routed out of the current network segment as it only has value on the local link and is there to provide services on the local link only. Or stated another way, no properly designed router (i.e. L3 device, like your firewall) will forward traffic from a local link address off the local link.
So, yes, a device with a local link address that is infected with malicious software of any kind should not be able to reach any device not on the local link. As such it would not be able to spread the malicious software off of the local link.
However your described situation has a number of flaws. The first and foremost is that 169.254.0.0/16 address should not be assigned manually or by DHCP server to any device, as per RFC3927. This will make any sort of configuration difficult (if even possible in the first place) and subject to interruption in the process should the associated address change.