I haven't proofread this, so let me know if something doesn't make sense.
I I was born and raised outside of Palau, but I am of Palauan descent. I don't have many specific answers to most of your questions, but I'll try to answer them as best I can.
If you're on Facebook, there are several online communities that are fairly active and you might get better answers there. Palau does have a US Embassy (sorry for assuming you're American) with a Facebook Page and I'm sure they'll be able to answer your questions better than I can.
Please be advised that Palau's internet is behind the times (literally dial-up speeds), even at the internet cafes, which is the most common way of accessing the internet. They only got 3G this year and I've heard it's relatively expensive. Mobile phone options are very limited as well. PNCC is the only provider and you must purchase airtime (calling cards), which is sold at most retail stores.
Accommodation - how much could I get accommodation for 2 months? It would be me & my girlfriend
It's not very expensive or difficult to find a place to stay as long as you're not living in a hotel. It's a developing nation so the standard of living may be may be much lower than your used to.
How do you get around the island? Is there public transport?
As far as I know, public transportation is non-existent. It's a very small place and there's only one main road in the Koror/Airai place, which is probably where you will be staying. A rental car is probably your best option. Although they're inexpensive, the price of fuel is insanely expensive. Like most countries, they drive on the right side, but most available vehicles have their driver's side on the right side as well. It might feel strange at first if you're not used to it, but it's not difficult to adapt.
What is there to do on the island for leisure time?
If you love the ocean, Palau is the place to be. A tropical climate with unparalleled in beauty. If you're into SCUBA diving, you'd already know that it is among the best of the best in the world. If you like the idea of SCUBA, but have never diving you've never done it, I'd suggest getting certified it as soon as possible. It's not a cheap hobby, but you definitely won't regret it. You are probably aware of the Rock Islands and Jellyfish lake already. If not, you will be. If you like fishing, you're love Palau. But from what I've heard, it's just not the same as it was 15-20 years go.
The night life isn't the greatest, nor is the selection of beer. If you're into good beer, Palau is not the greatest place to be.
Is it expensive? What are the typical prices for food, drink, meals, activities etc?
Food and drinks are expensive because everything has to be imported, except for seafood. Fresh fruits and vegetables? Forget about it. I love Palauan food because I'm Palauan. But culinary refinement is not exactly Palau's forte.
I read the language is Palaun & English - will there be a huge language barrier if I just speak English?
You won't have much trouble holding conversations with native Palauans under the age of 40 and almost all of them will have many relatives living the U.S. (who are probably in the US military). However, you may have trouble communicating with foreigners, most of whom are Filipino, Taiwanese/Chinese, and Bangladeshi. The demographics have changed so much since I was a kid.
Any hints or tips about your culture?
Again, most Palauans are very familiar with American culture, so they won't be offended by your unfamiliarity with our culture. Palau is such a small island and there are so few of us in the world, that most Palauans would love to talk to you about our culture.
Thank you for your time!! If I do come (as I hope to), then I shall take you out for a beer or two!
I would love to take you up on that offer if I were actually in Palau. But again, Palau's beer options are limited to Budweiser and a few big Asian beers. There is a local brewery (ie, Rooster), which in my opinion is palatable, but leaves a lot to be desired.