Does he accept you as his son?
Yes, of course he accept me as his son. He was the one, who mentioned the option of the DNA test ("only a DNA test could tell this"), when I visited him a few months ago at the house, where we grew up. He still lives there. He even invited me to eat some sweets at the nearby cake shop (I could freely choose a dessert, he bought two of my choice for me - a slice of cake -, plus he also bought a soft drink chosen by me, and he also bought some for himself), and gifted me a syrup bottle and 2000 HUF (currently approximately $6.70 USD) ($1 USD is currently 298.40 HUF) to "buy something more than the train ticket home". I still have some of the syrup.
Based on our meeting, I have a very strong feeling that he is my real father, and I also think that a step father would not do these things.
I have a paper from the hospital, in which I was born. His name is written in the field of "Father (or guardian)". But there is another name on my birth certificate. The name of my (step?)father, who died in 1997.
Why would the hospital write the name of my stepfather, instead of the real one? Why would I even have a stepfather at the time of my birth?
I have so many questions.
I checked online and they do have cheap DNA tests for $49 USD
Where we live, the test is around 55 000 HUF, which is approximately $184.32 USD.