Hi and welcome!
Here are some answers to your questions:
1) How is the healthcare? Should I go with a private general doctor or the public one?
VT-> There are a lot of private healthcare services like Thorax and Vita(you can check for their websites or send me a message, as I'm not sure I'm allowed to post link here) still you can go to lots of other doctors that have private cabinets(almost all) as long as you pay.
2) How easy/hard is it to get a driving license? I know how to drive I just dont have a license.
VT-> I'm afraid getting a driving license requires some knowledge of Bulgarian. You should probably try to get a validation for your driving license in Bulgaria. If you start from the beginning it costs around 400 euro and takes around 1-2 months(depending on schedule, driving school, etc) to pass the courses and get a driving license
3) Anyone have any leads on a good apartment near Vitosha street? Looking to spend maybe 400-500 euro on a nice apartment with proper kitchen.
VT-> You should check appartments when you arrive here. For bulgarians the usual way is to look through the biggest real estate sites and start calling. Unfortunately there are tons of fake ads on the websites, so you should really spend some time visiting properties. But for your pricerange, you can get a decent apartment. For example I live around 10 minutes driving distance(25-30 walking one) from the start of Vistosha street for 300euro. Keep in mind that appartments are usually provided with flat rate for the rent only. Electricity, gas(you better get apartment with air conditioning or gas, as the winters can be quite cold) are not included in the rent. I can get you in contact with a great broker for the south neighbourhoods(but will need to check whether he speaks proper english) or you can get a local translator to help you the first days
4) How is cable television? Are there digital boxes? Do services like netflix work in Bulgaria?\
VT-> There are many providers of digital television. The largest are Bulsatcom, Blizoo, Megalan, but depending on where you live, you may be able to land on a sweet deal with some local provider. Usually there are a lot of packages for internet and television combined
5) Any recommendations for good gyms or personal trainers in Sofia?
VT-> There are a lot of good gyms, but it all depends on where you will be living. Keep in mind that public transport is not so nice as for example in Germany. It is good, if you don't need to travel around half of the city for a decent gym. Some of the best: Sport city, The gym, Pulse and some more
6) Any recommendations for good tattoo artists in Sofia?
VT-> Not really in my competence, but I think there are quite a few studios and you can ask around when you arrive. People are usually keen to talk about their tattoos and Sofia is not a very large city, so it will be easier to find out
7) Are there any institutes where I can do night classes to learn Bulgarian?
VT-> Probably there are, but you can get better and faster results with some foreign language schools. I remember Bravo schools offered something like that. Additionally a lot of bulgarians in Sofia speak english very well and you can learn a lot from them trying to speak in Bulgarian and getting feedback in english. Unfortunately I don't know a lot of foreigners in Bulgaria that speak bulgarian fluently...probably because they are good with english and get a translator for administrative services, etc
8) Anyone use a trustworthy apartment cleaning service?
VT-> There are quite a few. Vasilka being one of the top in the sector, but you can get some local do the same job for less money, if price is important
9) Are there laundry services that pick up/deliver your laundry?
VT-> It is not a very popular service in Bulgaria. Probably there is, but you can usually easily find a local laundry that you can leave and then pick up your laundry
10) Are there any facebook groups for young professionals living in Sofia?
VT-> Depending on the area you are working in. There are more for IT professionals for example, but facebook groups are not quite popular. Also betahaus is a nice place probably where you can meet young focused people.
Let me know, if I wasn't clear enough on some of the answers, I'll be happy to help!
Have a great time in Bulgaria!
Ventsislav Tomev