Is Speech lower in use or dependent on other factors? I have currently 50% Speech but when I talk to people the Speech option often shows a much lower %-value.

E.g. when talking to the Megaton Sheriff, Lucas Simms, I only have 21% when asking to get 500 caps for disarming the bomb.

I have only 1 Charisma, does that influence Speech beyond the sole skill % bonus?

Well, you see, each Speech check has a difficulty. Not many are as easy as others, and you won't get them all. Charisma really only does what you said.

Some speech checks are harder to pass, even if you have x speech level. With that said, having 1 Charisma will also greatly impact your chance of success so the percentage of you passing is drastically lowered, in addition to your speech level.

I thought every Speech check has a fixed threshold you need to pass. Like you need e.g. for lock picking or hacking. Isn't that the case in FO: New Vegas?

It might be the case with Fallout: New Vegas, but this is Fallout 3, a different game.

Speech checks in FO3 are percentage-based. The higher your skill, the easier it is to pass a check, but if you were to save and reload, you could pass all Speech checks in the game with 1 Charisma and 5 Speech. In fact, I'm pretty sure that's the reason New Vegas uses the hard pass/fail checks: you could pass every Speech Check in FO3 without the slightest investment in your Speech skill. More Speech just meant fewer reloads.

Anyway, as has been mentioned, Speech Checks in FO3 have some sort of difficulty modifier behind the scenes that affects how likely you are to succeed. Apparently there are some checks that are very difficult to pass, even with 100 Speech.

yep speech checks are changed by many factors. Karma (good vs evil), charisma, and a few other factors and some of those factors don't even show up in the "shown" percentage to pass. For instance it might show 25% chance to work, which means logically 1 in every 4 chances or so should pass the check, but you might try and pass it for 20 times and nothing will happen because while it might show 25% to you, it really might be 3% based on different factors so you are thinking you really have a 25% chance while its not really that.

Good thing is, you can just reload and keep trying eventually you'll pass it.

That's nothing to do with the way the game works and everything to do with independent rolls. The game doesn't care that you failed the last 167 attempts on a 50% chance. All it cares about is that the RNG keeps giving you a bad roll. Each roll is factored separately from the roll(s) before it, and has no effect on the roll(s) after it.

and again, a person that obviously never took any classes on percentages, odds, or logic. Do a little homework before saying silly arguments that RNG number rolls are based only upon themselves and rolls before and after have no effect on odds or probability. A simple google search will prove you wrong without me even having to actually give you the mathmatical formula for such things, which is annoying having to do it 100 times for people with no knowledge on probability and odds.

Just go to any gambling website with the formulas. Has NO basis on what ever RNG theory you are pondering about in Never-Never land. We live in the real world with real facts thanks.