*Door entry systems place addition barriers for all those with communication difficulties none more so than for Laryngectomees.
There are a couple of errors in the sentence. "addition" should be "additional". There should be a comma after "difficulties", and there should be two additional words "and for" in front of the word "none". The "for" in front of "laryngectomees" could be removed or left in.
Door entry systems place additional barriers for all those with communication difficulties, and for none more so than for laryngectomees.
The meaning is that "laryngectomees", those who have undergone a laryngectomy and are unable to speak, are among those with communication difficulties who are inflicted with the extra barriers. "None more so" means that none of those who have communication difficulties are affected worse than the laryngectomees. That is, they are among the most affected.
Q1. In the corrected version, "none" is the object of the preposition "for". It isn't a subject.
Q2. I hope the addition of "and for" will clear this up. "places barriers for X and for Y", where "X" is those with communication difficulties, and Y is laryngectomees.