In my research, I didn't find set dates to do X, a lot of it is tied to soil temperatures and other conditions. Texas A&M, Clemson, Auburn all have published recommendations on when to apply fungicides, pesticides and weed preventatives for Zoysia. I was able to find them pretty easily with Google. That said, I typically aim for September - October for fall pre-emerge, February-March for spring. Watch soil temps. When they get to and below 70 in the fall, it's time, the reverse is true for spring and you're looking for it to creep above mid-50's. On fungicides, I've been told for preventative, at or around Labor Day and St. Patrick's Day are good benchmarks and then as needed according to conditions. The only set pesticide applications I do is in the spring, Talstar at the first sign of ant and mid-July, Merit for grubs.
And no, I don't know of any reason you can't fert when you're doing your other treatments. Now tank mixing it all together is another thing. You'll probably want to research that pretty closely, depending on the products.

 

https://extension.uga.edu/content/dam/extension-county-offices/forsyth-county/anr/ZoysiagrassLawnCalendar.pdf

That should have some of what you're looking for. Maybe you already found this, since what you've listed isn't in the calendar

 

Thank you both for the information!