You only get one "Bonus" trait for choosing your initial aspiration, either in CAS or upon aging up to teen. In my experience, this doesn't ever change. There are also "Reward" traits that you get for completing aspirations, but they don't become available until you complete the final tier. Some of your issues sound like bugs, but a few of them just sound like standard game mechanics working as intended. You can switch your aspirations any time without losing progress on them, but your bonus trait stays the same no matter how many times you switch/complete aspirations. At least that has always been my experience. If you use enough Potions of youth and/or skilling boosts, you could theoretically unlock all of the reward traits for completing aspirations(though it would be tough because some of them conflict), but you wouldn't get all of the bonus traits, only the initial one. I'm open to correction, but I don't think that's a bug. I think tha't the way its supposed to work. Otherwise it would be highly exploitable and you could just cycle through aspirations to get a bunch of free traits. It should also be noted that you don't have to complete apirations to switch to a new one. I'll do the lower tiers even on ones I don't want to complete just for more reward points. I also tend to complete multiple aspirations so I have a fair amount of experience with how the traits work.
The one caution I would give is that you should never accept a birthday party invitation from one of your inactive Sims (they sometimes occur randomly over the phone). Allowing a sim to age up this way does not give them the opportunity to pick their trait/aspirations and leaves you at the mercy of the rng. It is also the only case I've encountered where a Sim doesnt get a bonus trait at all. Since they don't choose their initial aspiration they just don't get a trait for it even if they switch to a different one.