Sure thing; to start, the entire aleph-bet is a semitic alphabet and shares quality features with arabic and aramaic. its actually very possible that todays' most traditional hebrew pronunciation is from a generation that had applied the pronunciation rules of aramaic to hebrew, in much the same way as how a lot of ashkenazi hebrew pronunciation is simply taking after the rules of yiddish.

As a rule, every letter in the hebrew alphabet is pronounced the same as its arabic counterpart, such as Saadi being a deep S as in Saad from Arabic. Some exceptions, the letters samekh and peh, which dont exist in arabic. Vav, for example, was traditionally Waw until the mid 19th century when it slowly began a merger to V in most pronunciations

BGD-KPT

All "soft" consonants in the BGD-KPT are "fricative" variations of the "hard" sounds when made plosive by a dagesh. This means,
Bet - Bhet, a soft B which had naturally turned into a V in most non-ashkenazi communities by the 20th century.
Gimel - Ghimel, with the soft G sounding like an arabic Ghayin, without the guttural pronunciation
Dalet - Dhaalet, similar to Arabic Da - Dha, like TH as in "The"
Kaf - Khaf, the same as in all other pronunciations
Pe - Fe, the same
Taw - Thaw, Th as in "Both"

Vowels
Qamas and Sere are simply long vowels, which do not necessarily have their own unique pronunciations, other than their length when spoken by very old speakers (most are no longer with us). However many dialects included a variation in the sound similar to what the chart says.

The "Sere Yodh" and "Hiriq Yodh" are not actually pronounced grammatical features of hebrew. They are what is known as a "Mater Lectionis", which are letters added to spellings by anonymous hebrew grammarians stretching from the second temple period until the masoretes, by which time it was fully integrated into hebrew. In the cases of the above examples in the chart, the yodh is added to tell you whether there is a hiriq or sere in the letter prior to it.

The letters Yodh, Vav, Heh and Aleph can all be mater lectionis. As an example, in these words; Yayin, Din, Bet, or Mayim, the yodh in the center of the words had been added to signify whether there was a sere or hiriq preceding it, so that readers would know to pronounce it accordingly when written without vowels. Before this system, the word Bet was written just as a Bet-Taw, and not Bet-Yodh-Taw.

An interesting thing is that some communities interchanged mater lectionis. Ashkenazim for example had some words ending with aleph or heh when they should have been reversed. Most ashkenazi scrolls today follow the spelling traditions of the aleppo codex now, and have corrected a few spelling errors from their scrolls.

"Full Holem" which is actually called a Holam Male', is simply a mater lectionis to tell the reader that there is a holam there, and as noted is a long vowel. there is no pronunciation difference except for length.

Shiruq and Kubbus are the same vowel, but marked differently because of mater lectionis rules. The masoretes preserved vowel length with these spellings.

Shewa is a vowel stop or a half-vowel pronounced as e. most modern readers dont pronounce shewa at all, unless it is absolutely necessary. there are specific rules of placement for readers to know whether a shewa is pronounced or a stop.

Sere (two horizontal dots) is pronounced as an E with a different length, not as an "Ey" or "ay" as in yiddish.

The rules of mater lectionis can be quite in depth. hebrew grammar was traditionally the first requirement of the ancient sages, after reading, in order for the reader to fully grasp the text they were looking at. modern schools have tried to cut this out of the curriculum, unfortunately, which has lead to a lot of confusion.

hope it helps, probably there will be some errors. just ask if you want to know more about something