I notice deep cracks on hardwood floor all over like below. We really like the house and buy it. Is this a major problem or a common one
The scratches in your photo are not a problem - they are a feature. Yes I'm being serious.
It is common to find hardwood flooring these days which is intentionally 'distressed' by creating these scratches & grooves before being finished - and you can see in your pic that the finish on this flooring extends down into the grooves, and has not been scraped off.
Sometimes the features are intended to look like old well-worn flooring, and other times they're intended to look like the flooring was 'crafted' by hand. Often the features look like the remains of being rough-cut by a circular saw blade.
Take a trip to any flooring store in your neighborhood and look for the section featuring 'hand-scraped' and 'distressed' options - and you'll find many examples of what you're seeing here.
A google image search for "distressed hardwood flooring pictures" shows many examples:
Those are really deep scratches, you can't fix those completely. You could get rid of the smaller ones and fill up the bigger ones, you'd need to sand the whole floor down and refinish it though or it would look worse. At the end of that it may not look that much better, then the only option is replace the whole floor.
If it was me I'd invest in a rug which would cover that area, or I'd just live with it.