Some partial answers (I'm not a pro)
- Pros I've seen use 1" pipe from the meter to the valve box and 3/4" for long runs out to the heads. I can't quantify it but I'd imagine using 1/2" for everything, out to multiple heads as far as 150 feet will reduce flow and throw. Whether that's a problem is up to you (more below).
- You probably need a backflow preventer unless your bib already has one so whether or not you use the existing 1/2" pipe, it seems worth the effort to properly and permanently plumb in the backflow and from there the feed to the valve box.
- A hose bib splitter will be relatively unreliable, may fracture or leak and is not designed for continuous unattended use. It'll be the achilles heel of your system.
- If you're in a cold place you'll need to winterize and that definitely rules out a hose bib adapter. You need a solid shut off and an air valve that can withstand blowout pressure.
A few more thoughts on using too-small pipes:
Go find an online introduction to sprinkler system design. Get yourself to "Idiot's Guide" level. Your goal is (presumably) to have a healthy lawn in a reasonable and practical way. That means you need your sprinkler heads to cover your entire lawn, to provide an adequate amount of water everywhere, to do that with a minimal number of heads, and you want your watering program to run completely during periods when you’re not taking showers, washing dishes, and so on so your family is not competing with the sprinklers for their comfort.
So: Reducing flow and throw means you need fewer heads per zone, more zones, more heads and they need to run longer to water the entire lawn effectively. Running longer means running into shower times, or running all through the night which I've read promotes mold.
If your head layout was designed by a pro with a view to getting this right, there will be a presumed flow and pressure at the farthest head that will be based on a professional-style installation, using appropriate tubing and fittings.