Is New York Times conservative news website?

Answer 1

Not really. Interestingly, in the old days, the New York Times was in fact very corporate and somewhat conservative; it took very traditional positions on such issues as women's rights or gay rights. But these days, the Times' editorial pages typically takes a more liberal (left-wing) stance on social issues, and some of the opinion writers also express liberal views. But much of the newspaper's reporting of news is known for being objective and thorough.

That said, if you are seeking a conservative news website, I strongly recommend the magazine The Weekly Standard, or the editorial pages of the Wall Street Journal, both of which are reliable and reputable resources for conservative points of view.