Riku was NOT brought by AtW or anyone but Sora. Sora and Riku's hearts were resonating with each other, so Riku was brought to CO. Sora entered through just a regular door to the castle, no special DttL or a light realm door. CO is located in Twilight, not necessarilly inTT, but in Twilight.
Vexen was able to create the RR because he's a scientist. He was able to make a lifelike puppet (and he stole the recipie for making a heart from Feinklstein! jk) and he put a heart in RR and made Namine create false memories.
There are only 12 basement levels, the top (number 13) is the main level where Sora entered from (not the exact room BtW.)
CoM story follows SDG as they go up CO reliving their memories with a twist, kairi is no longer in any of them. (And yes, kairi had something to do with each and every level on KH1.) As they proceed up the castle, Namine (Kairi's nobody) is slowly moving around the chains of Sora's memories and adding false ones. When he beats all the Org members, Namine promises to give Sora his memories, but Sora has to go to sleep. So Sora goes to sleep. Some time before Sora reached the top of the CO, Riku entered in from the basement. He makes his way up the CO basements fighting off Ansem inside of him, and the RR. The worlds he travels through are worlds that he went to, and that Sora went to. The first four are worlds that Riku went to in KH1. Riku is told by Malificent in HB memories that all that's left in his memories are of the darkness, so riku vows to destroy all the darkness. His sole purpose of going through the other worlds is for him to be able to destroy the dark memories becuase he wants nothing to do with them.