>Kokoro: Co-core-oh (co as in co-pilot.) I think Co-ca-row (Yes, with the first two like Coca-cola.) is probably the correct one, but I like my pronunciation better.
Remember that Japanese is a syllabic language. Each syllable is well-defined, and will always sound the same. "Ko" will always sound like "ko", so two "ko"s in a row will sound like "cocoa" (with a silent a).
Additionally, syllables in Japanese never end in a consonant sound. Even the "n" that you see at the end of some "syllables" (eg senpai) is treated as a syllable of its own. And, on that note, "n" is the only consonant which is treated this way. You will never see a syllable pronounced like "core" in Japanese.
Using this information, we can break "Kokoro" up into the following syllables:
So, once again assuming a silent a, "Kokoro" should be pronounced similarly to "cocoa row".
While we're at it,
>Tewi: The first one, otherwise you would write it as Tei. (Eientei is written differently, but the connection is interesting to consider and I'd accept it for that.)
Once upon a time, Japan used to actually have a "wi" sound. Now they don't. "Wi" is a chararacter that isn't actually ever used, and in fact isn't even taught to most foreigners learning Japanese. Since it appears in old texts, they still need to be able to use it, and they approximate it by just saying "i".
The closest thing Japanese has to an actual "i" sound is the dipthong "ui". Japanese dipthongs are strange in that the "u" and "i" are actually separate syllables, but are often spoken quickly in a way that merges them into one voiced syllable. Spoken at a slower speed, it would normally come out as "ooh-eee", but when spoken quickly it comes out closer to the English word "we".
>Dai: Die-yo-say. I usually just use the first syllable when I can be bothered to remember her at all.
Very close. "Dai", "you", and "sei" are actually two syllables each. Da-ee-yo-uu-seh-ee (ee pronounced as in the English word see). Again, the dipthongs are often spoken fast enough to sound like single syllables (die-yoo-say, remember that the u doubles the length of the o!), but they're actually two.
This. Similarly to how Japanese r sounds are actually l sounds at the same time, "ji" and "zi" are also the exact same sound. When you pronounce that character, you pronounce it as sort of a blend between those two sounds.
"ji" is what you get when you voice the consonant on the syllable "shi". As English speakers, we have a tendency to want to pronounce this the same as the English word "she". This is correct, but it's also correct (if uncommon) to pronounce it the same as the English word "see". In fact, the proper pronunciation is kinda both of those at the same time.
The other s sounds in Japanese voice in a pretty straightforward way. "sa" becomes "za", "su" becomes "zu", "se" becomes "ze", and "so" becomes "zo". However, since "shi" is already a sound that doesn't quite fit in with sounds we're used to in English, when we voice the s in "shi", we end up with a sound that's really strange to English speakers.
That said, it's actually pronounced a lot closer to "zi" than "ji". Why is it often written as "ji", then? Because the syllables "jya", "jyu", and "jyo" (or simply "ja", "ju", and "jo") are made by combining "ji" with a y sound (for example, ji fuses with ya to become ja), and these are pronounced pretty much exactly as an English speaker would read them, with a J.
As for Cirno, because of how ambiguous it is, I just flat out ignore the fact that it's supposed to be a foreign name and pronounce it in Japanese: "chi" "ru" "no".