I’m traveling from Burgas to Istanbul for just one night - is it possible to see everything and what should I focus on most?
No it's not possible to see "everything" In one night. I spent seven nights in Istanbul and there was still a lot that I did not see. But depending on how much time you have, you can certainly see some things.
When you say one night, how much actual time does that entail? Do you have any part of a day to see things? If you're interested in the mosques, it would probably be best to stay near Sultanahmet, which is the tourist area but near to many of the major sites like Hagia Sophia, the Blue Mosque, Topkapi Palace and so on.
What you should focus on most is what interests you. Again many people want to see the beautiful mosques there so that might be an option. But there are other sites as well. For example, if you're interested in the whirling dervishes, you could arrange to see that.
Really, I think your best bet is to get a guidebook and look through the section on Istanbul. Most guidebooks have a top 10 list of sites to see so you could focus on that and see what interests you
In addition to Mardee's great advice, what you can cover also depends on the day of the week (some things are closed/open late), what time of day you arrive/depart, when you need to get to the airport (45-60 minutes from the historic area, arrive 2-3 hours ahead of flight), and where you plan to stay in Istanbul. Then you'd need to decide what you are interested in seeing and trying to fit that into the actual amount of time you have available in Istanbul.
This is Rick Steves' take on Istanbul: https://www.ricksteves.com/europe/turkey/istanbul The "At A Glance" lists sites in the City. Under "Plan", "Recommended Itinerary" starts with a 2-day Itinerary.
A few months ago I had a 24 hour layover in Istanbul. I laced together the RS walking tours and it made for an exhausting day but I was able to "see" most everything. With the time that I had (one full day) that made the most sense for me and allowed me to go at my own pace and see what I wanted int the time that I had. This was my route: Historic Core walking tour, then Old Town Back Streets walk; then tram to Taksim Square for the New District walk. I was pretty tired at the end so if I had to do it again, I would skip the New District walk unless you like shopping.