Easy comebacks ?

[Belacqua]

Exactly where it says that christians don't believe in old testament now (or in some parts of it) ? 

Most Christians believe in the Old Testament, but not all of them in the same way, and not as a set of laws that are binding on them. 

they don't believe in world created in 6 days, don't believe that Moses existed? 

It would be interesting to discover what percentage of modern Christians believe in a literal 6-day creation. Certainly not all of them. Are you thinking that all Christians are sola scriptura literalists? That would be an oversimplification. Augustine, for example, wrote a whole book on Genesis, advocating a more careful and allegorical reading than modern creationists.

Moses may have been a historical figure. Some Christians believe so, and some don't. Some see him as the representative of a type, and don't care whether a real person of that name lived. 

They just wanna pick less gruesome parts now, right? 

For a very long time Christians have interpreted the Old Testament in different ways. It has been customary, for example, to read each statement in a four-level hermeneutic. So while the literal meaning is the most obvious one, it may be that the message they want to take away is a moral, allegorical, or anagogic interpretation. 

So Christians who limit themselves to the literal meaning will have to accept the gruesome parts, but since non-literal interpretations have been common from very early on, it's common for less simple-minded Christians to reject violent meanings. Warfare may be seen as internal, spiritual struggle, for example, just as jihad in Islam may be a moral struggle within oneself. Or Plato's Republic may not refer to a real city government, but to a well-ordered mental state in an individual. 

It's also worth mentioning that for many Christian readers, the level of interpretation they call "literal" is not necessarily a simple reading of the obvious sense. When Augustine talks about a literal reading, he means he wants to interpret the sentence according to the intention of the original author. This means, paradoxically, that if the original author meant a statement to be metaphorical, the literal meaning would be metaphorical.

It's not as simple as you may be imagining.

Where god says that "gays is good now" in  any of religious christian texts after old testament?

I think I wrote before that "gay" is not a concept that people in biblical times could use. They condemned acts, not orientations. It's true that people of that time looked down on sodomy. But it's also true that many many Christians in our own time are accepting of different sexual preferences. It would be a mistake to assume that all Christians are the same as the worst ones.