There are 16 characters in the game: eight females and eight males. James (the Rainbow Mode character from Singles 1) did not return and Josh, Magnet, Anna and Kim are new. (the picture is Rotobee's work, not mine - click it to see the large version)
All characters behave pretty much alike. Some are messier than others, all have different likes and dislike and all have a different default outfit, but aside from those differences, their behaviors are pretty much identical.
In free-play mode you have three characters to work with, so mix and match to your heart's content. Want a swingin' bachelor pad? How about trying to recreate "Sex and the City"? A menage-a-trois? Go for it. Just keep your Sinlges satisfied and they'll be putty in your hands. Invitees are another issue entirely, but since I know that you're the original silver-tongued devil, I'm confident that you will be able to handle any difficulties they might pose.
Leaving aside cheat extensions, there are a few things that you should know about the 13 characters that you aren't playing. First off, in order to be able to "call" someone, you have to meet them in the bar. No matter how good your relationship with them may become, having one of the other roomates invite them over will not add them to another character's "call" menu. If the relationship is exceptionally good, they will often appear on the "invite" menu, but not on the "call" menu.
Secondly, invitees will not brush their teeth or take a shower at the apartment (the devs apparently didn't think to provide spare toothbrushes or towels). You can make them do these activities with a cheat extension, but they won't do it unless you can take control over their actions. They will cook, eat, go to the toilet, wash their hands, entertain themselves and even do their laundry (if you can overcome the third issue), but not brush their teeth or shower.
Thirdly, invitees will not stay longer than 24 hours from the time that you invite them. You can ask them to leave or order them to leave (which drops your relationships with them) to make them go home earlier, but they'll stay no longer than 24 hours. You can always invite them back after they have left the building (which is how I found out about the laundry thing), but 24 hours seems to the limit for a visit. If a player character invites them to bed (the relationships have to be decently high for them to do it), they will sleep afterward and stay overnight. If this goes longer than 24 hours, they'll leave when they wake up (and without the decency to make a pot of coffee before they go).