I'll split this into parts per your various questions.
=-0-=-0-=
> Anyone here have a Speech Impediment?
In early public grade school [1st-4th grade after being first noticed during Kindergarten] I had to go to the school's speech therapist; I had a speech stutter plus a mild lisp against the sound "sh" as in "shut up", a worst lisp against the sound "ch" as in "chimney", and a medium lisp against pronouncing the letter "h" as in "e-f-g-H-i-j" not the actual sound as in "Hairy Henry".
Naturally, I hated being pulled out of class x3 a week for the speech therapy; it just screamed "Hey that kid's SPED" ("SPecial EDucation") and I knew it, and I also knew it wasn't doing me any favors on making friends [the prospect of bullying for "not talking right" be damned, that just wasn't a concern for me then against actual social interaction and social familiarity being time-limited -- don't ask my how I understood this so early on, I just did]. When I switched schools in the middle of 4th grade, I still had to go to the speech therapy but then also the "catch-up sessions" for "being academically behind" too, so now I was forced to double-down on being pulled out of class. Not Good, as now I'm "Double SPED". I had to get out of that crap and the sooner the better; I had to Be Normal [which became a Life Goal, as rational or irrational as you need that to be], especially as the New Kid who just switched schools in the middle of the bloody school year.
Before that school year ended, fortunately, I managed to talk my way out of continuing the speech therapy by explaining this "SPED Stigma" to the teachers, parents, and speech therapist involved [I realized the pun of phrasing it this way only 2-3 years ago, and decided to keep it for the telling here]. I got to skip the speech therapy for the rest of time and agreed to just grit my teeth through the Catch-Up sessions until summer came. Luckily enough I had "caught up enough" to be treated as a normal student from 5th grade onward. My stutter was an occasional treat instead of an Always Thing, and the "sh//ch//h" pronunciation issues were just what they were gonna be at that point with no additional helping to be had.
By University it was clear to me that my stutter was going to manifest itself when I was overly nervous, overly excited, or mentally impaired [e.g. migraines, booze]. That's fine, no one cared or cares. For the pronunciations, guess what? One single person since 4th grade asked if I "had a lisp" and simply because he was honestly curious and we were cool at the time; if anyone else has ever noticed, they've kept their mouth shut to my face so that's all whatever on that front.
I bought a copy of "The King's Speech" after seeing it in theater. The scene with the record-player and headphones in the therapist's office, and the climactic scene with the globally national radio address, are touching.
Last year I went to a ComicCon and quite randomly got an autograph from Matt Frewer... AKA Max Headroom. I mentioned that my olde speech therapist from grade school mentioned his character numerous times in attempts to get me to be comfortable and at-least be less self-conscious, and he mentioned how whatever the national "speech therapist stutterers association of America" group at the time kept calling in to the show with good will. He also gave an obligatory compliment toward how I spoke, which I of course very much appreciated. Yes, I promptly framed the autographed Max Headroom picture with no regrets.
> What about your work, phone calls, and The Dread Pirate Presentations?
My work isn't negatively influenced. Sure, I get nervous during presentations I have to give, but since I'm aware of my own stutter whilst nervous I add in the pauses and other mental gymnastics that can help my speech; I still get error but I'm ok with that for now. Still, no one cares enough to mention; I'm still not a card-carrying member of Toast Masters, but I do listen to The Moth.
I've never had problems with conference calls or meetings; sure I'll double-up on stuff like "... what, what about XYZ?" or "But that's, what's that gonna do about ABC?", but that's normal enough conversationalist phrasing to not blip on most people's radar and no one's said anything to my face about it.
=-0-=-0-=
> Work with people with speech issues?
I knowingly have not as far as my memory is concerned, but a few years ago I did interview at a place where one of the higher-ups who interviewed me did have a severe stutter. "Stage 4", honestly speaking.
Obviously I was sympathetic and patient -- because of my above history, not necessarily because I was the on the short end of the power dynamic -- and asked for clarification on anything I just couldn't understand from his stutter as if he had had a very heavy accent instead. He seemed used to such interaction and took it in stride. I still felt uncomfortable, a lot of it due to my sympathy and empathy for him; we both had no illusions about what was going on -- there's a severe stutter here, he's clearly making an effort to being understood, I'm clearly making an effort to understand, so let's do this -- but since I was on the short end of the power dynamic I didn't want to play the "I just can't understand you" card every two minutes [yes I needed clarification at that frequency at a minimum if not sooner it was that bad].
Note: I wasn't provided an offer for that gig but it had nothing to do with this guy's stutter or my opposing behavior toward it; this was simply a Bad Fit all around and I have little regret over it.
The "good news" here is that at this company there's a higher up who has a severe stutter; people clearly have the patience [or tolerance, or professionalism, or whatever thesaurus equivalent you want to use] to have this guy around creating value.