So I'll go a couple items on that list, but the first thing that popped out at me was this, "This list is subjective, and based on news reports rather than peer-reviewed articles in scientific publications". Basically, the article is warning you to take all it's claims with a grain of salt. On to the list!
10. Asherah was a Semetic deity worship by several of the ancient peoples of the Levant, including the Akkadians, and was considered a wife or consort of the Hebrew god YHWH before they became monaltrists. The book of Jeremiah, written c. 630BCE may have referred to Asherah in Jeremiah 7:16-18 and Jeremiah 44:17-19, 25. Just because a popular regional "real" (at least to her worshippers) deity was mentioned in the Bible does not automatically "prove" the Bible. It's a fallacy equivalent to saying that a certain issue of a comic book shows Captain America fighting Adolf Hitler; Hitler was a real person ergo we have proven Captain America is/was a real person.
8. Herod was a real historical person, attested to both by contemporary records and contemporary historians. For an explanation of why this does not prove the Bible, see #10.
7. The Bible is set in or mentions several real historical places including Jerusalem, Jericho, Egypt, and Gath. The fallacy of saying that being set in a real place "proves" a work as true is so common it has a special name, the Spiderman Fallacy. The Spiderman Fallacy works like this: the Spiderman comics are set in New York City, which is a real place; therefore Spiderman is real.
Now, mind you these are just the ones that jump out at me and I'm writing purely from memory. Two of the items, numbers 9 & 4, deal with things outside the scope of the Bible, so I don't understand why they would be on the list of archeological finds "proving" the Bible at all. #9 describes a Jewish site from the Byzantine era, well after the start of the Jesus cult; #4 describes a Caananite (not Hebrew) item.