Hey! I have plumbed my share of tanks and can offer some opinions to your questions
1. What should I use for sump baffles? Can I just use aquamesh or something porous or does it need to be glass or acrylic?
The type of baffles you would use all depend on your goal for those baffles. Baffles are usually the same material that the sump is made of (i.e. glass sump -> glass baffles). The baffles are used to regulate water level and flow. That being said, baffles are not necessarily needed. There are plenty of threads showing successful tanks with a baffle-less sump.
If you use porous style baffles, it would only be there to separate the chambers and not regulate water flow or water level. This is fine if all you want to do is set up barriers in between the different sections of your sump. Water level will stay the same throughout the whole sump.
2. How do I keep a stable water level in the sump and how do I "set" this level?
Stable water level depends on the sump type. If the sump has baffles, all chambers, except for the pump chamber, will have stable water levels (although the sump chamber usually has an adjustable baffle to regulate water height). The pump chamber keeps a stable water level by either having an automatic top off or manually topping off evaporated water. The water level is set by filling up the sump and only looking into the pump chamber and adjust the level while the pump is running.
In a baffle-less or porous baffle sump, the water level is constant throughout the complete sump. The water level is also kept stable by using an ATO or doing MTOs. The water level is set by filling up the sump to whatever level you desire while the pump is running. If you plan to have a refugium in this type of sump, then I would adjust the water height to the height that will support the refugium and then adjust the skimmer to the height that is optimal for its operation. You might need to put it on a stand.
3. Is there anything I should change about the design? Again this tank may not even happen but if it does I want to make sure I've got a good foundation. I want to try and use more "natural" filtration methods with lots of macroalgae and living parts in the sump instead of chemicals like GFO or something similar.
The sump design looks fine. It's a standard design that is used in almost all commercially available sumps.
Again, if you are planning to use a refugium, I would design the baffles to keep the refugium in place. Certain macroalgae's stay in place because they attach themselves to a solid surface (rubble rock, etc.) but others are free floating and need to be kept from getting into your other chambers, causing a clog in your tank or skimmer. Same goes for sand or mud. If you plan to use either, you will need to make sure the water flow will not disturb the substrate, blowing it all over your sump and eventually display.
Hope this helps.