Is there any reason I should expect Tabhair (to give) to be pronounced toor (or choor)? Are there are other words where abhai turns into an "oo" sound?

Thanks so much! I've been learning Irish for awhile now from Duolingo, Learn Irish/ Bite Sized Irish youtube, and some CD's I have, but I think it's time I start posting to this forum with my questions.. So expect to see more of me around! Peace out!

Tabhair is pronounced túir, yes.

This verb has various suppletive conjugated forms (like "I go" and "I went" in English, which have different origins, but are now in the same paradigm). Tugaim, tabhair and bheirim (an older form of tugaim) are in the same paradigm.

The original had as the absolute form "do-bheirim".
The absolute form means the form like táim that is used where not following certain particles; the dependent form is a form like fuilim used after ní, an, nách, go, etc. So in the verb "to be", there is "táim" "níl <ní bhfuil" and "an bhfuil?"
In a similar way, this verb had do-bheirim in the absolute. The dependent was "ní thabhraim" or "ní thiúbhraim" as it was once written too. This is because the dependent forms often had a different stress to the absolute. do-BHEIRim is absolute, but the dependent saw the stress put in on the first syllable: DO-bheirim. The ú pronunciation derived from the pronunciation of this DO- once the following bh is vocalised.

Wow! Not going to lie most of what you said went over my head haha. But is it fair to say that the pronunciation of this word is because of the historical evolution of where the word is derived from???

I'm just trying to understand how "phonetic" of a language Irish is. Like, whilst trying to read Irish, how often can I just sound a word out, and how often will I have to have experience with that exact word if I'm going to be able to pronounce it correctly.

Not a very phonetic language, but maybe more guessable than English once you know the system. But the fact there are three main dialects with different pronunciations makes things harder. Most learners are recommended to pick a dialect and imitate that pronunciation. A good source of pronunciation is https://www.teanglann.ie/en/fuaim/tabhairt, where you can pick the dialect. In this case the pronunciations are quite similar for this word. But if you look at the pronunciations for oíche mhaith (good night) at https://www.teanglann.ie/en/fuaim/o%c3%adche_mhaith, you will see they are quite different. So that site will help you a lot.