Do I still need the "bridgeport simbot fix" mod to make simbots in bridgeport if my base game version is 1.24 or it's been fixed by EA already?
Do I need to be self-registered as an Inventor to get the opportunity to make the simbot or I just need to get to level 10 inventing skill?
Can I send a simbot to work, make him join a career?
Can I make a simbot immortal? if yes, how? If no, does he eat ambrosia and get the effect?
Yes, it appears that this is still required.
No; the opportunity will arise irrespective of what career you have.
Yes; SimBots can work. They are usually very well-suited for an Inventor career, in fact. ;)
If you have Generations, the Age Freeze Potion lifetime reward should do the trick nicely.
If not, Ambrosia should give the desired effect.
Additionally, it's worth considering NRaas' Story Progression mod; which, besides being a pretty great mod overall, also comes with the option of making SimBots, (and vampires, mummies and ghosts) immortal.