Greetings from across the pond.
What you are suggesting is possible with some chemicals and not others. Youtube content like Doc and Ryan Knorr have a place int he community as it gets people interested in lawn care. A lot of those folks try some of that stuff then end up here.
Spraying something like Prodiamine or Nitrogen (think miracle grow) is possible with a hose end sprayer, and yes a hose end sprayer can be calibrated if you can get one semi consistent for a little bit. That said, Prodiamine isn't critically accurate in it's application and is meant to be a soil application.
Some of the other things you are talking about, 3 way herbicides, fungicides...etc, they are meant to be foliar applications and applied via a fine misting and left to dry on the leaf blades, something a hose end sprayer just can't accomplish.
Can a hose end sprayer get you started with Pre-emergent and fertilizer applications? Absolutely. Is it going to last you long term and help in your weed control? Definitely not.
I have 2 acres of property and am proof you don't need a high end barttery powered backpack sprayer. I do have a 25gal sprayer for my atv but I also have 2 4gallon pump sprayers that I use for a lot of my applications when I don't want to rig up the atv with the tank and all of that hassle.
If you're going to take the time to get into lawn care and try to apply herbicides and fungicides with a greater degree of effectiveness then just throwing down some granuals, you simply need the proper equipment. I love making things work, this just isn't one of those things you can kind of make work. Again, some products, yeah sure, others, no, you can literally kill entire trees in your yard by accident by over applying just a small amount.