What is the name of this style of knife?

While that knife is not one I'm familiar with (as interesting as it looks), there are a few knives I do know of that have the handle directly above the blade. It transmits force very cleanly, you're right, it makes it much easier to leverage for cutting. The ones I've seen are curved, for a rocking rather than slicing method of cutting - but you might find it interesting to look into them anyway, either as well as your knife, or if you can't find the same.

You might look for "Ulu" knives, which are found in Alaska (and nowadays, online, of course). It is an all purpose knife, its actually the first knife of this type that I found. There are a couple variations, including slightly different curves or handle types, but the standard one is shown below.

Another type of knife is the "mezzaluna", out of Italy. Many of these tend to be two-handled (although ones similar to the ulu in shape do exist), which will give the option of more force, instead of trying to two-hand the little handle of the ulu (center of force is your whole torso), or more control over the rocking motion. Others, will have more than one blade mounted next to each other, the set of two or three blades meant to quickly cut finely - often for herbs, but no real reason you couldn't use it to cut anything else if you wanted, twice as much slicing per cut. And finally, there exist much larger versions (where the two-hand grip really works), which might be used for long, controlled cuts (like a pizza cutter or something).

And finally, you might look up "vertical grip" knives (also vertical force, or vertical handle) - this will get you to some odder knife shapes, maybe from modern day re-imagining or re-engineering for ease of use, or maybe intended for assistive use (for those with reduced abilities or the like) - but if you like them, no reason not to go ahead and look. one site which has a few is here.

I believe it is a frozen food saw. The serration is very small like you would need to saw through frozen fish for example. Given that it was made in Japan, I believe it is a YAX brand knife/saw. While I couldn't find that exact style from them, they did make some that were very similar.

Google Image Search "yax frozen food saw" and you'll see several.

This is a frozen food knife or a bone saw. It is made by YAX. It is very similar to the knife you are asking about. At times you can find one on EBay. Hope this helps and good luck.

If you like knives that have this similar grip, you can look at menkiri knives:

It is not exactly the same as what you are asking for but has similar control leverage and force that you described.

Furthermore, I am actually searching for the name of a similar type of knife, which I post here: Does anyone know the name of the knife this ice cream seller is using?

Hope someone can answer it too!