I'll do my best to answer all of the questions posted, if I missed one just let me know!
How many players are typically in-world at a time?
Like most games it depends on the time of day but it varies between 150 and 300 normally. On a night that a social ball is being held, it can go much higher but that is due to a lot of two-boxers (dual accounts) getting social points on more than one character.
Can you ride a horse? Tame pets?
There are no animals in the game for the very specific reason of not wanting to promote or encourage beastiality.
Hire NPC bodyguards?
As for hiring NPC bodyguards, no but you could hire other PC's to be your guards if you wish. Since the whole social and govermental system is run by the players, many of them hire PC's to be their guards so this is not unheard of. The Prime Minister for example, always hires PC Bodyguards because just holding that position gives any player the ability to PK you, so they typically go no where alone.
Can you own a house? Build a house?
Own yes, build no. There are a few different styles you can get, but they are all premade rooms in apartment buildings. You can furnish them with items made by either yourself or other players, but not change the configuration of the structure itself.
Can you outright refuse to participate in some activities such as PVP, rape scenes, etc?
Well, yes and no....
There are three levels character type: Newbie, Casual and Full (PC). PC is the highest status, no limitations.
Newbies and Casuals are invulnerable to attack and rape by a Full character ONLY IF they remember to keep their guard up. Guard can manually be dropped to allow someone to "carry" you somewhere. What some do not remember is once they have a hold of you, they can do what they wish with you. You can try to struggle to get free, you can declare them as hostile but at that point, it is all about the mechanics. Being raped by an NPC is also a possiblity depending on what your characters sex urge is and how satisfied it is.
When signing up for the game and agreeing to the EULA, it is understood that there is a threat of murder, rape, attack etc. There is no official way to officially "opt out" of any aspect mechanically. HOWEVER, what I have heard of players doing was just log off or walk away from the computer if they are grabbed in that type of situation.
In the over 3 years I played this game, I was raped only once. If you read the forums for the game some will make it sound like rape is rampant, but it's not. It's all about the circle you hang out with and actions you take. Yes, there are some players that will rape/attack just because they can, and give it no RP value, but those you will be able to target quickly and get awayfrom.