Hello Shambhu,

Hope you're doing fine. You can definitely pursue your engineering at 23. However to pursue the same, you need to clear the requisite entrance exams of different colleges (like JEE Mains, JEE Advance,  VITEE, BITSAT, SRMJEEE, or state based entrance examinations based on the state you are from).

Depending upon the entrance examination, the age limit changes. For example, JEE Advance  allows only 2 attempts, more precisely one attempt during your 12th and one more the next year, but there are many state and private colleges that do not have this barrier.

Now coming to your second question, Yes you will face certain amount of difficulties during campus drives because many companies have an upper age limit. However, do not get demotivated as there are many off-campus drives that you might opt for.

Hope this helps.