“free”: As in free beer? yes. As in freedom/free speech? no!
“not limited”: wrong! it limits who can use it. if you work for a competitor of lt (now analog) then you are not allowed to use it at all.
“supported”: I would call it “published by” in this case as support implies some hotline that you can call or at least an open bugtracker. (There is however a quite large community out there because it is the most powerful “free” simulator at this point in time.)
Lets hope ngspice will get a boost from being “used” by kicad such that it can compete with ltspice in the near future. That would finally give us a truly free (as in freedom) circuit simulator.
No it is exactly the other way round. Freecad for example is free as in free speach. It uses LGPL as the license which guarantees that. (similar with ngspice and kicad or even linux.)
Ltspice on the other hand is only free as in free beer. You do not have the freedom to modify the software to your liking. You are not even allowed to redistribute it in an unchanged form should analog ever decide to stop supporting it. (well you can not redistribute it now either but right now there is no real need for redistribution.)