No they don't just push out, you will need to roll the inner lip out while putting pressure on it. I start at the top corner and put the whole top out.
Reusing the seal really depends on what kind of shape it is in. Whether you can use it also depends on what kind of slider what in it. If you can wrap it around the glass and it seal up, yeah it will work, some sliders had a wider seal though.
For reinstalling, run a 1/4" nylon cord around the sides and top, drop the bottom in and with pressure from the outside. I sprayed a little water in there to make it slip out easier last time...