Does Charisma have any real impact besides skill bonuses and Perk requirements? Are there charisma checks in dialogue or can I get by with an obscene Speech? Does it affect followers?

Does Luck increase likelihood of random encounters?

Charisma Helps in the area of companions, barter(?) and speech. Luck increases your chance of random encounters (I think) and with your critical hit chance. I need to look more into both for more info.

I did a little checking and found the following in one of the many Fallout Wikis:

http://fallout.neoseeker.com/wiki/Charisma

I specifically looked for Fallout 1 info and even though it seems to refer to the other Games in the Series, I'm pretty sure it applies to Fallout 1.

I got by in my playthrough with an Average Charisma and Tagged Speech. I am pretty sure that a high Speech more than makes up for anything you lack in CHA & even if you decide to go with a high CHA, you still want to put a lot into Speech.

As far as Luck, it is supposed to increase the chances for random encounters, I know it seems to do a little more in Fallout 2 than 1 but I've only played through once so I don't really have a way to compare from experience. A high Luck definitely increases the chance of getting some of the special encounters that are in FO1 and those are a lot of fun.

[url=http://user.tninet.se/~jyg699a/fallout.html]Per Jorner's Nearly Ultimate Fallout guide[/url]

I wouldn't trust the Neoseeker page too much, it seems to be talking primarily about fallout 3 and new vegas.

Anyway, the relevent section is this:

It's also strange that Int affects the number of anwser you can do when you talk to NPCs. I know it makes sence, but if it that factor was affect by Char, this skill would be less useless

You can sleep with a woman if you're male and have 7+ cha, but besides getting a few free drugs this won't have an effect on the game. That's the only cha benefit, so playing with only 1 is fine, int and speech are checked for dialogue, not cha.

Char increases the max number of NPCs you can have in your party (in Fallout 2 only).
1-3 = 1 NPC
4-5 = 2 NPCs
6-7 = 3 NPCs
8-9 = 4 NPCs
10 = 5 NPCs (It's the max you can have in your team. Dogmeat and Miria doesn't count as NPC IIRC)

Don't forget that you can always use mentats (and the sunglass) to increase the max number of NPCs, so you don't need high char to have many followers. : )
Unless you want to make a diplomat, I wouldn't advice to put many points in charisma.

Luck increases the chance of finding special encounters, your luck in combat (with low luck firearms can explode in your hand : P ), and your critical chance. Don't put 10 in luck, unless you want to take the Sniper or Slayer (<- luck 10 isn't necessary to always do crit. hits) perk. Your luck also increases Gamble skill, but in my opinion, it's useless and you shouldn't waste points in it.

CH affects nothing other than your base speech skill in F1.

And in F2, barring the companion count, there are very few times it will override your speech skill. Only instance I can think of being SPOILER::: before the fight with Horrigan, if you have high CH you can convince some Enclavers to fight with you :::SPOILER.

I'm pretty strongly of the opinion that a borderline good charisma can be the difference between a free lesbian tryst with the prostitute or a lonely night of self-congratulation if you manage to get the ideal ending for the hostage situation in Junktown. The game does detect whether you're male or female at that point, but she doesn't always care. Charisma seemed to make the difference for me.
This is not actually important. Just saying.