This area had been this way when I bought my Home. How can I replace or patch? Do I need a professional?
You need to make a larger patched area by lacing in the same width and type of wood you now have, then spot finishing the floor to match the rest of the existing floor. This Old House has videos at Youtube
You can get estimates from pros to do this (I would, I don't have the skills, tools or patience to do it myself) if it looks a little daunting. Those are beautiful floors!
You can use wood from a closet, that probably will match it. And who cares about inside of closet you can use new wood in there.
Lorraine, That is just brilliant!
Matching will be hard because the seams will always show. Why not use contrasting wood run in strips perpendicular to the main boards, in a pattern like parquet? You might even look at parquet flooring blocks which you cut into about 2 inch strips and lay the strips in a stripe, then finish off the end near that white tile with short pieces of board like the rest of the floor.
The hardest part is finding wood or stain to match your existing floor. I'm adding a video of This Old House doing a patch.
I have matched colors with stains and it's not that difficult.
I'm sure there is someplace close to you that sells used wood flooring.
Give it a try, you can't possibly make it look worse.
I like Lorraine's idea of stealing a closet's floor. I had to patch a floor and instead of trying to make it match I just painted on a "rug". It was cute.
I've done it..the idea of using wood from a closet is a good one. Its VERY time consuming, but is worth the effort. Not having a professional's tools is not a deal breaker. Just make sure when you are nailing the boards in (on an angle) you predrill the holes so as not to split the wood.
Take wood from closets
Lorraine is right, take the wood from the closets in the home. No one sees them in full light so if they are newer boards you will not really notice it. We did this in our house and it worked out great.