Yes, President Obama can appoint someone to fill the Supreme Court seat left vacant when Justice Antonin Scalia died in February 2016. It is by law Obama's appointment to make, with the advice and consent of the Senate.
The New York Post and the New York Times are daily newspapers that publish 365 issues a year -- 366 on leap years, and the occasional "extra" edition in the event of world-shaking news, like the 9-11 terrorist attacks. The New Yorker is a weekly magazine that publishes 47 issues per year and covers news, the arts, culture and anything else of interest.
Yes, Senate Republicans should allow a vote on whoever President Obama appoints to succeed Supreme Court Justice Antonin Scalia, who died in February 2016. If they don't, they'll further erode public confidence in the Senate and the Supreme Court.
The New York Post is a reliable newspaper. When you compare it to other newspapers, the main differences between the Post and, say, the New York Times are ones of tone, style, appearance, choice of story subjects--its personality.