You will not be able to recreate the tank in the picture you provided without co2. You do not need co2 to make a planted tank work, but it speeds plant growth... like 10 times as fast. Additionally there are plants that will only grow with co2 and others that will grow without co2 but their behavior is drastically different. Some red plants won't really "redden" up till they have co2. I am going to assume your light will work fine since its a reef light. You will want to be careful you don't blast too hard when starting up. Planted tanks are all about balance. If you have too much light your plants will need more fertilizer and more co2. If you do not have all 3 in equal quantities then you get algae.
I am not clear on your substrate preference. Do you prefer dark substrates? Or are you asking if that is what planted tank folks prefer?
If the former there are a LOT of options. Eco-Complete is very popular and you will find the reviews of it very polarizing. Some like myself hate it because its jagged, difficult to plant into, and (in my opinion) is not aesthetically pleasing. Others love it and use it in all their tanks. There is a gradient between the two views as well. If you live near a Tractor Supply store you could buy a bag of black diamond blasting sand. Its inert like eco-complete but a lot cheaper. Pretty popular as a diy option for black substrate. If you want darker colors that aren't black there is a range of gravel options as well. etc etc. The list of substrates that could work for you is quite long. But they break down into active substrates (substrates that release nutrients into the water) and inert substrates. Active substrates tend to be blackish in color. They are things like ada aquasoil, control soil, etc.
If you are looking to keep fertilizers simple then something like Thrive is a good option. If you decide to go with no co2 then ThriveC is the way to go since it has liquid carbon in the formula.
If you are bound and determined not to use co2 and you want a carpet then you are most likely looking at either dwarf hairgrass or crypt parva. Both can grow without co2 but carpeting.... well you either plant super heavy to start (5 times more expensive on plants at least) or you wait years for it to grow in. A kind of middle ground is doing a dwarf hairgrass carpet using the dry start method. Basically you grow the grass while there is almost no water in the tank. Assuming you do it right you could have a carpet in a couple of months. Lots of options you can look into.
Whether you need to screen off an overflow depends on what stock you put in the tank. If you are planning to breed shrimp then taking some silicone and attaching a piece of stainless steel mesh over the inside of an overflow may be a good idea. Similar issue if you have fish small enough to fit into the overflow.
Generally planted tanks want 4 to 8 times an hour turn over of water. Whether your pump can do that will determine if you can just use the existing filter.
I will say that planted tanks pretty much never run carbon. The reason being that it will suck the fertilizers out of the water the same way it would other water contaminants. Sponges, ceramic bio media, pot scrubbers, whatever you want but typically not carbon.