Talk to people? No, I don't think there's ever been punishment for talking to someone your old character knew. It would be bad form to simply step in as an existing, long-time friend of your old long-term friends, but it sure isn't against the rules.
Now, if you had made your friends the Commanders/Managers of your ships/facilities, and then they gave them all over to your new character, then that would definitely be against the rules!
As for the thieves lists, they are affected somewhat by OOC (having to list IRC nicks for certain people who don't use their handles, etc) so listing a previous character as a thief simply goes to indicate the moral quality of the player. However, a character should not be condemned as a thief solely on the fact a past character of the same player stole.
It may, of course, come up as supporting evidence in a new theft accusation against a subsequent character.
"May the Grace of Ara go with you, and His Vengeance be wrought upon your enemies."
I don't know of any thief lists that list a new character as a thief based on their old character, and any that do so are probably not to be trusted in the first place due to their ability to distinguish IC from OOC (the only exception being players who still use the name of their old character on IRC and need to be distinguished on that basis solely as a means of identification). It has always been policy for a returning player whose past character was a thief to be given a second chance on his subsequent character.
What about if your a faction leader, get killed or die, and then want control of your faction? Say Vodo Bonias or any faction leader is arrested and executed..... when they create a new character what would happen? Would they just be like every other newb? Would the combine team be understanding and promote them back to faction leader? What?
When a character dies and a new one is created they are on the same level as every other newbie. Some players make the OOC decision to treat them as such, whereas others would happily give them a higher position on the basis that they're already experienced, are friends, or something else entirely.
The Combine "team," assuming you mean the staff, would not hand the new character the old character's faction.