JEE

Yes, you need to. AI is a stream of Engineering in which either Integrated course of AI or B.Tech in Robotics is available in India. But most of the colleges which provides AI designing contains Integrated course facility. Admission is these colleges is through counselling based on the marks / rank

As there is no FIITJEE, Bansal, etc. you should go for GATEFORUM or Engineers Academy. They are really good.

You can join private universities like VIT, Manipal and SRM because your JEE score is not too good for any good government college. You should try for private ones rather than the government colleges.

It depends on your branch preference and also which IITs you consider as "good". Cutoffs are much higher in old IITs of Delhi, Kanpur and Bombay than the newly opened ones. JEE Board offered ranks to students scoring above 123 marks in JEE '14 which went approximately to AIR 19000.
However, general

It'll depend on what branch you want. With 104 marks you'll get biotech, biomedical, print and media technology, automobile and aeronautical mostly. With 51000 rank, you'll get biotech and biomedical at SRM.

You cannot get a good college with your score. But don't worry, you can check your options of getting colleges here. Go to the link given below:https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Hello,
You can check the list of college including NIT and IIITs you can get according to your marks and rank here. Use Shiksha JEE College Predictor:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=cconnect&utm_medium=CR_JEECP&utm_campaign=7489993

Hello,
You can check the list of college including NIT and IIITs you can get according to your marks and rank here. Use Shiksha JEE College Predictor:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=cconnect&utm_medium=CR_JEECP&utm_campaign=7489993

You can get admission there if you belong to a reserved category otherwise it is nearly impossible.