. . .. I think they are able to continue fighting (basic attacks) once they arrive at their target and make their initial attacks . . .
No, this is wrong, and is a 3e way of thinking. 'You think' they are able to continue fighting is not the same as them being able to continue fighting. The DMG is very explicit when it refers to mounts, and Martial Power is not as vague as you seem to think on the subject of companions. Each *person* gets a standard, move, and minor action. You, not your PC, you physical Ed-Zero gets the same actions whether you are controlling 5 things or one.
This could be unbalancing, if each of your three creatures had a specific thing at which they excel. If, for instance, you were mounted on a very fast mount, and you were very good at ranged attacking, and your pet was very good at melee, you could roam the perimiter (move) attack (standard), and allow your pet to take OA's and Immediate actions.
Jay