What does "take a call" mean?

The normal, simple meaning of "take a call" is to decide to receive a phone call. For example a leader of one country would 'take a call' from another to discuss some issue, as opposed to 'not taking a call' meaning that they don't want to discuss.

By extension the phrase can be used for any form of discussion, not just a phone call. So your first could reasonably be interpreted to mean that Sonia Gandhi will discuss the candidatures of relatives with others, presumably before making a decision.

I had thought that the in second sentence "take a call" was a mistake for "make a call". In British and American English "Make a call" means to make a clear and definite decision: for example a football referee "makes a call" on whether a goal is valid or not. However I have since found several examples of Indian English where "take a call" is used with the same meaning as "make a call" in British English, i.e. "make a definite decision". 1 2

While the company may be urging you to discuss with others whether you want to abide by their safety rules, it is much more likely that they want you clearly decide if you want to continue your business with the company (in which case you need to abide by the safety rules) or not.

The first example appears to be in the sense of "receive a phone call", in this case extended to mean "sit in on a conference call".

The second example appears to be a sports (or perhaps card game) metaphor, but it's hard to guess specifically which one. A player may be "called" for some sort of "foul", or (particularly in cards) may choose to "pass" a round of the game.

There are several other senses of the idiom, but those would seem to fit best.

This is a phrase peculiar to India. It's not used by native English speakers. Its meaning is the same as "make the call", i.e. to make a decision.

Here are headlines from two Indian newspapers that illustrate this usage:

• "Delhi government tells HC it will take a call on night curfew soon" - Indian Express, 28/02/2021
• "Will take a call on nursery admissions in 2-3 weeks: Delhi government" - Times of India, 27/11/2020

take a decision

eg: A man apprehended his girl friend is gay, "If she agrees she likes other women and sexually attracted to them, then you need to address your fears and take a call on your relationship.

To "answer the call," it means to metaphorically look within, and follow, what you refer to as "your gut" "your soul" or "your heart" is willing you to do. Take a chance, and lean into what you understand not.