I'm not a professional historian, but I do have some self-taught knowledge on Korean politics in the late Joseon Dynasty (I am also a South Korean citizen), so I had a look at free excerpts of the listed books.

Michael Seth's A History of Korea: From Antiquity to the Present

This seems to be mostly accurate; to me it seems a fine overview. However, like most overviews, it generalizes, and it is not immune to common errors and misconceptions or errors with dates. For instance, in the section about Joseon politics:

The late seventeenth century saw Korea ridden with factional struggles centered in the capital. The Namin (Southerners) came to power in 1674. They were ousted by the Seoin (Westerners) in 1689, who soon split into rival Noron and Soron (Old and Young Doctrine) factions.

First, it glosses over the complex history from 1659 to 1674 through which the Namin finally gained power in 1674. That is of course understandable in a book that is a general overview of thousands of years of history.

Second, as said, errors with precise dating seem to be present. By reading this passage, one would probably think that the Namin retained power from 1674 to 1689 until they were ousted. Not true - the Namin lost power in 1680 and key Namin leaders were executed the same year. The Seoin were dominant from 1680 to 1689, and in 1689 the Namin ousted the Seoin, not vice versa. A diminished Namin faction had power between 1689 and 1694, when it was ousted again by the Seoin.

Thirdly, it makes a common mistake on the foundation of Noron / Soron; the division between the two factions was clearly in existence by 1684, five years before 1689, though of course the tension was less marked than in, say, 1724.

Kyung Moon Hwang's A History of Korea

Unfortunately, Google Books e-books of this book is very limited (it abruptly stops around 1000 AD), but this book also seems to be a good enough overview. Note that it has limited information about North Korea (one chapter, compared to almost half a dozen chapters South Korea gets), and it is oriented towards more recent events; half of the book is set after the late nineteenth century. The content almost reminds me of modern South Korean history textbooks, which is only natural; after all, in the very first sentence, the author says "This book assumes no prior knowledge of Korean history."

Chun-Gil Kim's The History of Korea

I didn't really like this book. Though only the first 45 pages are available, I felt something wrong as I read it. The work seemed to have a stronger nationalistic bent than the other ones, for instance the use of the Korean term "Malgal" - rarely used outside Korea - rather than "Mohe", or discussing Mimana, a disputed term almost no people being introduced to Korean history would be expected to know about, in a general overview.

The Korean War books I've read are

Hastings: The Korean War
Fehrenbach: This Kind of War
Halberstam: The Coldest Winter.

Of these, I'd say that Hastings makes the best general overview. It covers many different aspects of the war, and is by far the most generous to the Chinese and non-American UN troops.

Fehrenbach is a great read, though it's clear that the book is very dated. The complete lack of any reference to Vietnam was actually really surprising to me until I realized that This Kind of War was first published in 1963. This book does a very good job of discussing why Americans performed so poorly during the early phases of the war, and also has some interesting things to say about MacArthur.

Halberstam is actually a fairly frustrating read. It hints at some interesting topics involving N. Korean-Soviet-Chinese interactions, but after the first chapter or two there author gets laser-focused on American actions between June 1950 and June 1951. There are some interesting bits about the Pusan Perimeter and Chipyong-ni, but next to nothing about the two year stalemate or the peace negotiations.