What to do if you join a company and leave it within the first 2/3 months for a different company?

Sorry to hear that you were laid off, but seems like you were able to get some good offers shortly after.

How should I notify the manager at company B and explain them the situation?

I'd just explain that you really love the new project/team/scope available at company C. Employment in the US is at-will so you don't need to worry too much about how to justify this. It's pretty common for employees to hop around. Just leave respectfully in such a way that you don't burn bridges.

How and when do I notify company C that I had to join company B to maintain my visa status?

Why does company C need to know this? No need to reveal anything that isn't necessary for your employment with company C.

I’m afraid that company C would think bad as I’m leaving a recently joined company B (what if the company C’s recruiter think if I will do same with them in future)

Are you getting any signal from the recruiter that they think this? Have you done this in the past? I wouldn't assume this to be an issue. If it comes up that you're leaving company B relatively quickly, spin it as a positive: "I'm really excited about the work at company C, and I felt like this was an opportunity worth jumping in right now for."

What if the company C does layoffs after joining them?

This is something you probably don't have control over, but you should evaluate the safety of company B vs company C. Take a look at this related question: https://www.jointaro.com/question/UCG4XxyEOTjjyg4pEuwY/how-to-evaluate-a-startup/

Is there a possibility to make sure anything(s) with company B to burn as less bridges as possible?

When talking about your decision to leave, focus on where you're headed (company C) instead of what you're leaving behind (company B). This way, you avoid saying anything negative about your previous employer, and it leaves the possibility open that you can come back.