To me, it looks more like solid wood planks. As mentioned previously, your choices are basically to sand it down and have it fully restored, which in my experience is expensive, or completely replace the flooring which might actually be cheaper. Might be a better idea to choose new flooring, maybe go with lookalike wood flooring that's a bit more hard ...
It appears that this type of flooring is not as easy find as I thought it would be. I do believe you can at least find a random width oak..... somewhere.... You can determine whether it is white or red oak by beginning to tooth out one of the pieces that needs it anyway, and look at the end grain. It if looks like it has a lot of tiny pinholes in the annular ...
Why do you want to identify the type of flooring? It looks like solid wood flooring. Are you looking to identify install type (floating, nail, glue down), wood species?
For a scratch like that I'd be tempted to just spot sand and try to buff a finish in that blends with the existing. In order to do that well you'd probably want to try sanding a board ...
You have two choices:
Sand down and refinish the entire room
Can be costly. DIY tends to produce terrible results
Remove, replace, and finish just the affected planks
If you choose this then you can more easily identify the wood once it is removed
The simplest way to fix the issue is what Jimmy Fix it suggests, or even a smaller version of what he has pictured by cutting down that material even smaller before finishing the same as the floor.
If you want it to look the way it does now minus the gap, that will be an entirely different matter.
It will require the removal of the original nosing, ...
Since that area of the floor will be under the new cable banister/rail, there would be no fear of creating a tripping hazard by covering the gap with a decorative wood strip. I would use a low-profile oak "carpet transition bar" type of strip, stained and varnished to match.
That is an expansion joint and it must be filled with a flexible material. The proper choice is a foam backer road topped with 100% silicone sealant. You can color match the silicone to the grout to hide the seam.
All edges need to be concealed by trim, whether it's baseboard, base shoe, transition strip, or termination molding.
In most of the cases you mentioned, a simple L-molding should do, such as against the stair railing board. Obviously your stairs are getting some new treatment or other, so that could serve as the overlay.
Consider cutting channels under ...