Are the X-Men dead? Are we going to see them again or Logan was the last?

No, the X-Men are alive. Logan happened on Earth 807128, where Earth-Prime is Earth-616.

There's already a New-Mutants movie planned(hopefully with X-23), and Deadpool 2 is also coming soon. For the X-men, there's no concrete plans yet, but most likely there will be a new X-men movie in 2018, or 2019. They will need to recast though, most X-men actors were under a 3-movie deal, so they need to reboot.

You have to remember.........NONE of the X-men movies were in any kind of logical sequence.........

Professor X was crippled in one, walking in another, crippled as Young man, in one, crippled as an older man later..........Jean is dead........no,. she's alive.........same for Cyclops.......

each movie has had a varying plotline and supposed "history". .....none connected to the last one.

So "Logan", might very well be the "last" story.....let's say of Wolverine's timeline......but they can still crank out "alternative" timelines.............different endings,......or simply focus on OTHER X-Men for a change.

they are not just gonna stop a multi-billion dollar franchise.

SInger is still contracted for another X-Men movie, this one focusing on the Dark Phoenix saga.

Logan is out of canon, so doesn;t count with the other X-Men films. They will continue with a sequel to Apocalypse.