Text in widget not centered

You can do this using CSS.

.wordpoints-points-top-users td {
   text-align: center;
   vertical-align: center;
}

You can copy that and paste it into the Additional CSS section in the theme Customizer.

It looks a little bit better now https://prntscr.com/j0x8mr , how to do same with my points widget?

I think this should work:

.widget .wordpoints-points-logs td {
   text-align: center;
   vertical-align: center;
}

Can avatar be removed from Top users widget?

Yes, this should work:

.widget .wordpoints-points-top-users .avatar {
   display: none;
}