[kmonster]

Don't bother about possible party members, with less than 6 charisma more than 3 are not allowed. Sulik, Vic and Cassidy are considered the best since they have plenty of hit points and can wear any armor to reduce damage taken, use their weapons effectively and equip better ones when you find them later in the game, can level up to improve their combat power and don't have special disadvantages like slow movement.
Which weapons NPCs can use depends on how the weapons are animated in combat, not on weapon type (Sulik can use a .223 pistol since it looks like a machine gun in combat for example) so its worth trying out when you find better weapons.
It's possible to have a 4th NPC join your party if you use drugs to raise your cha to 6, they won't leave if it goes down again.
But in the end only one character does matter: Mingan the Great Hero

A1: There are two casinos in NR (there's of course more than 1 area in NR), one is owned by the Mordinos and one is owned by the Bishops. You have to go up the stairs in the right one.
A2: With 80 doctor you'll succeed in all the skill checks, but you can't heal everything. If you're talking about the man outside Vault City, using doctor skill will reveal that he's radiated, using a rad-away on him will slowly help him over time. You won't get a big reward for this however.
A3: You have to talk to the shop owner outside Vault City.
A4: You can avoid the pariah dog joining if you run away before it spots you on the random encounter. Afterwards killing it is the only way to get rid of it. When it's dead everything will be as it was before meeting it, no lasting disadvantages. The "jinxed" trait can be quite fun since enemies will also have many critical misses, but on the long run it will get annoying.
The other dogs are just like the human NPCs, they won't join you on their own and can be dismissed.