You can run 1/2" to them.
They make fittings for that.
Ripped out all the old rusty galvanized pipes and replaced them with a Pex manifold and 1/2 " tubing. The question is can I run the 1/2 right to each of my sinks, showers and toilets or do I need to reduce the flow to 3/8" Can I reduce it right at the appliance with a 1/2 to 3/8 connection?
You can put a compression stop valve on the pex - the OD is the same as copper pipe. You need a reinforcement ferrule, which is packaged with a valve, or available in bulk if you get one packaged for copper. To make things more 'robust', it's nice to use a copper stubout for the valve. These can be anchored in the wall and provide good support for the shutoffs.
Important note - I'm not a pro
Retired Defense Industry Engineer; Schluter 2.5-day Workshop Completed 2013, 2014