1. Do I have to be a UAE resident to buy property in Dubai?
No, you can be a "non-resident" and still own property. Most of the developers will accept funds from non-resident individuals, and also offshore entities to purchase property. Law has been changed to allow "foreign" ownership.
2. You mention "offshore entities" - what is the main benefit of owning property through an offshore company? Is it not better to have the house or apartment in my own name?
The laws in Dubai are not the same as UK or EU. I particularly refer to laws regarding inheritance. When a foreigner who owns Dubai real estate passes away; the laws of the owners home country “should’ apply. I say “should”, as there are many cases where "Sharia Law" has been considered. Under Sharia law, upon death of a property owner, the property is generally transferred to the eldest male sibling. If you do not have a male sibling – then the property forms part of the state, and it is then up to an executor to go to court and get a ruling on whether or not this is correct.
A property owned by an offshore company would not be subject to Sharia law in relation to the distribution of assets, as long as the shares of the company are held outside of the UAE. This is because a company never dies. Shares can be distributed in accordance with the usual rules concerning succession in the place of the deceased shareholder’s domicile or Will. This is a very simple and cheap solution, that will, if nothing else, provide reassurance to a family.