Planting refugium, tons of questions inside

1) You will lose C02 with the wet/dry. The only way to minimize it, is to keep water drop and splashing down as much as possible.
2 - 3) Hornwort would work great. Grows fast floating or submersed and is a great nitrate sponge. In my heavily planted 75 gal., I have to add nitrate daily or it will bottom out in 4 days. I actually took the hornwort out.
4) Substrate is a matter of choice mostly. I use plain sand, but it is inert and doesn't really help heavy root feeders, but if using hornwort it will work fine.
5) I would put a diverter in and adjust flow rate as needed.
6) Algae will always occur in some way. Plants, ferts, and clean-up crew will all help minimize it.
7) I would start with about 4 hornworts and within 3 weeks you sould have to start pruning them to keep them under control.

When checking params on tap water, be sure to let it sit for 24hrs before doing tests.

1) If you make sure all the wet/dry media is in an airtight chamber (Think a 5-sided box with the open side below water level) You can inject CO2 into the wet/dry chamber and it will dissolve into the water.

2&3&4)another vote for hornwort. Just toss a bunch in there and put a really bright light over the top and you won't be able to get it to slow down, especially if you add CO2. You won't even need substrate. Just let it grow as a big mass free-floating in the water.

5) As I understand it you're going to have a wet-dry going into a sump, then a couple bulkhead fittings connecting it to another container where you'll have your plants. I'd put your big pump on the side of the bulkhead fitting closer to the wet-dry, then put a T in the line and run one side to your tank, and one side to the opposite end of the refugium, with a valve to reduce the flow rate to whatever you want. Then the water will flow through the refugium, and back into the main part of the sump through the bulkhead fitting(s). I don't know if that's what you meant by diverter, but I think that would be the most effective, economical setup.

Also, having such a low flow rate through the refugium... Instead of worrying about CO2 loss in the wet/dry, you could take the diverted flow from the pump and run it through a simple CO2 reactor with a DIY CO2 bottle or if you have a bunch of extra cash, a pressurized system. That way your refugium would be recieving a constant flow of CO2-rich, nitrate-rich water.

6) Your refugium should starve the main tank of nutrients enough to really slow algae growth, especially if you have standard lighting on the main tank and ridiculously intense lighting on the refugium (A single HID light maybe? or a bunch of those screw-in compact fluorescents? Or even a lighting kit from AHsupply.com.)

7) With any slow-growing plants, nutrient rich water like yours, and INTENSE lighting n the refugium, the plants should be growing so fast your fuge will be just a mass of plant matter in a few weeks anyway. Just keep it trimmed enough that light can get to all parts of the plants so you don't have dead leaves rotting and putting more nitrates back into the water.

If the refugium has clear sides, you could wrap it in mylar, and put mylar over the top of the tank (and over the lights!) in order to make the best use of the light you have available. Ultimately the more light you have striking the surface of the plant, the more nitrate you're going to remove.