You remove the baseboard, cut through through the old floor using a special kick space saw (they an go flush to a wall), tear it out, and then you can go up to the wall with the new, and the ends will be concealed by the baseboard.

Probably would have been easier to tear out the entire floor and install a solid 3/4" wood product. Hard to say if the guy is doing a decent job or not. I assume that the butt ends in the picture are significantly larger than the rest of the floors ends? With limited material available he is probably using every available piece. Is he fabricating the micro bevel on the cut ends? I wouldn't accept the butt ends filled with putty. After 5 days I would expect him to be getting the board ends to match the rest of the floor. You are gonna have to live with all the butt ends lined up like that. No way he could sand the boards flat. First, he would have to sand the entire floor to get it to be consistent finish. Second, the wear layer pictured looks to be less than a 1/16th No way he could sand that without going through somewhere. I would think that seeing as this is the same material being patched with that was originally installed there should be no difference in thickness, but I'm sure he's dealing with trying to scrap all the glue out of the tongue and grooves for each board. I'm not trying to beat you up, but this is another example for those considering a wood product for their floor where a solid wood product is far superior to this engineered stuff. We've done several of these repairs with solid products and they turn out fantastic. Solid wood products can be sanded and refinished multiple times, there is never an issued finding wood. Contrast that with engineered stuff where they are changing everything all the time. If you do choose this kinda stuff, make sure to buy a couple extra boxes to store away for these situations! Hopefully your guy can get this floor to your liking.

Use feather finish only to correct flatness if, you have uneven surfaces that is not within the manufacturer's recommended flatness tolerance. Otherwise, you do not needed.

I have a 17 year old marble floor. We are removing an entrance wall which leaves me needing eight tiles. I cannot find the exact same tiles. I found a travertine tile that is the same shape and tone. Would that work for the patching?