Learn English – has or have need to use if we talk about group of peoples

When talking about a national sports term, rather than a country, it's not unusual (in British English, at least), to use the plural. This is because a team is regarded as a group of people, whereas a country is not (companies also tend to use the plural; see also here).

So:

India have 11 players on the pitch.

suggests that we're talking about an Indian sports team.

Compare:

India has a population of 1.2 billion.

which implies we're talking about the country.

When using auxillary or helping verbs, the first verb is conjugated according to subject, but the second part of it is fixed.

Take present progressive tense, for an example:

I am going to the park.

He is going to the park.

We are going to the park.

The basic construction here is {to be} + {-ing form of verb}. The {to be} is conjugated according to subject, but not its helping verb - it'll always be "going" in this example.

This is the same with {to do} + {plain form of verb}, which is the emphatic form of a verb, and often used for negative and interrogative expressions.

I do go to the park from time to time.

He does go to the park from time to time.

Do you go to the park from time to time?

Does he go to the park from time to time?

Does anyone go to the park from time to time?

Anyone is singular, so the first verb is conjugated accordingly, but not any subsequent helping verb.