Is it possible to be born without a dad?

Yes if you are cloned like dolly the sheep. You probably wouldn't live very long or healthy there are certain genes in sperm that you wouldn't receive that would allow you to function normally.

You mean human parthenogenesis? I don't think it can really happen naturally but several groups of biologists claimed that they have been able to trigger it in vitro. Some of them were convinced of fraud, though.

Biologically no, In practice, yes as many children never know their fathers for one reason or another.

You need both a male and a female in order to produce a child.
However, if 'Dad' has previously partaken of a quick leg over without considering the possibility of the result, or taken no consideration of the suitability of the female to be a suitable parent, then panicked at the last moment and headed for the hills, I think that it can safely be considered that he has opted out of any responsibility for the situation.

Well I heard scientists can make 'premature' sperm cells out of bone marrow and they said they will be able to make active alive sperm cells from bone marrow in a few years

It is difficult to answer your question. It is extremely vague and you give no indication as to what you are actually asking.

Every human requires a sperm cell to get things started. That may come from the man your biological mother is lovingly and happily married to or it may come from an anonymous sperm donor. However, the sperm cell is required. Parthenogenesis does not occur in humans.

Can you be born without a man who will be involved in your life as your "dad". Yes, biologically speaking that is perfectly possible.

Dad is a social term. Lots of people are born without one.

Father is a biological term. Until genetic engineering is far more advanced that it is now every fetus has a biological father. Even mythical ones who claim otherwise.

Theoretically yes. But it doesn't happen in humans unless somebody would successfully clone a human. But it does happen in vertebrate other species, e.g. whiptail lizard.

http://www.scientificamerican.com/article/asexual-lizards/

No, the sperms, the male gametes are needed for sexual reproduction for a baby to be born.
The theory and law of science must be worked in this way, or it could never have happened.
(The male gametes are from the dad.)

You need semen to make a baby. So they could inject semen instead of having sexual intercourse. But you would still have a biological father who brought you into the world through his seed. So, no it's not possible to be born without a biological father.