Caesar's personality is akin to that of a mad scientist, coming off to Rex and the others as a tad out of whack from reality. Yet he seems to be aware of his own eccentricities as demonstrated when Rex asked him, "Are you crazy?!" to which he replied, "Depends on who you ask."
Although having no amnesia, Caesar has an information gap due to his five-year absence in sub-speed caused by the explosion blast at the Abysus research facility.
He occasionally talks off subject, easily distracted, does not seem to listen when spoken to directly and sometimes forgetful in daily activities. For example while he and Rex were trying to escape from Abysus, out of nowhere he asked Rex if he would like to see a photo of them and their father, Rafael. Caesar is also very upbeat, curious and quite over-protective of his younger brother. In fact, it seems some of Caesar's less "weird" traits are shared with Rex, such as his sense of humor and loyalty.
Despite his logical, and scientific tendencies and mentality, Caesar does show an open-minded side, to himself, apparently believing in the String Theory enough to try and create a Null Void Gun, and even believed in alien's enough to apparently believe (or at least take into consideration the possibility of) Ben's watch being alien in origin.
However, Caesar has shown to lack emotion at several instances in the series. For example, Caesar seems to be fearless, as long as science is involved, as he was not afraid of the mutations due to his work on nanites. As he had previously mentioned, he and his colleagues had expected mutations, but nothing like the present E.V.O.s and had stood in front of many without worrying about being harmed. Thus far, it seems that he is generally not afraid of anything, as made apparent by not only the E.V.O. situations, but the way he barged into Providence without prior worry
Caesar disappeared when the Org invaded Rex's world. The Society eventually discovered that's he very much alive, and is being held prisoner by the Organization. The Generals are already working on a rescue plan.
As for Caesar, Padro Lodo has him working on several new types of Nanites, including a new version even more dangerous than the originals.
Caesar was reluctant, but Lodo has more than 100,000 survivors from Rex's world as hostages, and if Caesar doesn't do his job, Lodo will "test" the Nanites the Org has produced so far on them. Plus, Lodo will dedicate a lot of resources into bringing Rex into his lab, and chopping him up for parts, which he can do.
Caesar seems to have comply, but Lodo knows better. He knows Caesar's working on a way out of this, but Lodo's already put several backup plans just in case.