Can I do a PhD without MSc? I am currently an undergraduate student in Turkey. I will graduate from genetics department and I would like to do a PhD without MSc in abroad. However my GPA sucks ( probably it will be 2.5 or 2.6 out of 4 ).

I have done my summer internships in Germany and America. I am very good in laboratory and I think I have got enough knowledge to do a PhD in genetics. My English level is upper-intermediate and I definitely have good references ( I have talked with 4 people, they are all Prof. and they all said that they would give very good references ).

But I am still concerned about my GPA. What do you think, can I be accepted to a PhD program?

Also, can I apply for both MSc and PhD or will they think that I am a fickle person and don't accept me for neither of them?
Some places in continental Europe can accept people with BSc but without MSc (but most - don't). In UK and US, MSc is a part of PhD, so typically you do don't need one to start.

But you ALWAYS need to consult a particular university/institute, as rules vary (and especially with treating foreign diplomas).

However, if your "GPA sucks" then, unless you have a strong research track (i.e. strong recommendation letters from your research internships, published papers) special exceptions may by unlikely.