1. How easy is it to find a furnished apartment in the city.
While it is not hard to find a place, be aware that Dubai is a very expensive place, in some areas even more so than the US. Many folks who work there, tend to live in the neighboring emirates and commute to work. ofcourse if your employer gives you accommodation, thats a whole other issue.
2. How necessary is a car or could I rely solely on public transportation/taxis to get to work, go to the market etc.
Again it depends on where you live. buses and taxis are not bad, some public transport is not airconditioned which is terrible in the heat. A car is good to have, but some apartment buildings do charge extra for parking spots, so make sure you know that ahead of time.
3. Do I need to pay taxes in the USA on the money I earn in Dubai.
If you are a US citizen or green card holder and file taxes here, you need to pay tax on your income earned there.
4. Would my age (44 years old) hinder my job prospects.
You will find differences in the work ethic as compared to the conditions here. The US has probably the fairest and the best rules on equal opportunity, and the best merit based job assessment and assignments. Of course no place is perfect, but there are rules for appeal in the workplace here that are probably the best in the world. Dubai is NOT as good. I have worked there and I know.The unspoken hierarchy is Arab nationals--> Arab non nationals-->whites-->Asians. If it sounds like overt racism it is and folks often know it and leverage it in their own interests. There is also a strong element of sexism.Younger is always better if one is looking for an unfair advantage. Differnt nationalities form cliques and are pretty clannish. A woman has to be actively assertive to hold her own in the workplace there. The employment rules are not fair, so be sure you negotiate your contract well going in. I had fought for my rights, but at the end of the day my workplace was not a happy place to be. I made a lot of money (tax free, as i was not a us citizen then), i make less here now, but I would still pick the Us as a better place to work in.
Hope this helps!