I can understand how you feel about the long hours and tough conditions.
To answer your main question first: Yes, you can take your friends advice, resign, leave the country and re-enter getting a visit visa at the airport - assuming that you are Greek. Cypriots need visit visas which are pre-arranged, BUT :
Even if you do obtain an employment/residence visa with a company, you are still legally allowed to resign during the probation period without any repercussions. The probation period by law is 6 months unless your contract says otherwise. Finally, please note that no bans are imposed on anyone who leaves a company and whose visa is terminated, especially from any of the 'Free Zones' - Media City is one of them. In fact, bans have pretty much been done away with in Dubai Emirate. As for deportations - you would have to do something criminal for anyone to do that.
As for working conditions, please note that you can find a better schedule - the usual is 9:00 to 6:00 - but the traffic problem is not going to go away and commuting is always going to be tough. Additionally, few jobs truly allow you to leave on time. Working a little bit more is pretty standard in the UAE, as it is now becoming standard in Athens and other major cities in our own countries. Why am I saying this: because I want you to approach any job - this or any other you find - with an open mind. Seek something which you enjoy to do, but don't expect the impossible - long hours and traveling time are pretty much a part of life in Dubai now.
To find a good job, do send CVs directly to companies in the industry of interest to you, but also approach some of the recruitment agencies available. I would look at the papers - the Gulf News has a great Careers supplement - and target all recruitment companies which have big adverts for jobs you consider interesting. Try to get them interested in you not just for that particular job. Also, go to the internet based ones: www.monster.com, www.bayt.com, www.gulftalent.com are some I recommend. As an HR Consultant I would be happy to offer advice on your CV and on agencies of interest.
Do let me know if you need any further advice or suggestions.