Is "to do well" used more frequently in India?

Personal thoughts

As a native Brit, "to do well" sounds perfectly normal to my ear; I suggest it is a generic English phrase, rather than a particularly Indian-English phrase.

Research

• Random example of the phrase, from an education website, whose contributors appear to be based in the USA:

Her child is in a local public school and without prompting from me she added “he’s doing well” to the end of her statement.

• Thesaurus entries for "do well", especially under the tab "prosper" sound perfectly natural equivalents to me:

prosper, bloom, flourish, thrive

• Its usage from google ngrams compares favourably to these synonyms based on the American English corpus and the British English corpus.

• Googling "team doing well" brings up plenty of results; none on the first page seem to be from India.

Conclusion

My personal thoughts are borne out by evidence: "to do well" is a generic English phrase, rather than a particularly Indian-English phrase.

Some fervent discussions in the comment thread. Interesting to read!

To answer your question - YES, To do well is a commonly used phrase in InE. It is associated mostly with performance (like performance in sports, performance of stock markets, performance in academics and the likes, as you have referred in your examples). However, it might be an Indianism which sounds odd to native speakers(where to do well means something entirely different). For instance, there are quite a number of Books to crack competitive exams and interviews that are titled

• How to do well in CAT

• How to do well in GMAT

• How to do well in Job Interviews

etc. in the Indian Book Stores. Implying, how to score higher grades or how to crack job interviews, performing well.

Here's a Ngram for "to do well" which shows that it is a regularly used term

In my personal view, searching in google(in domains like CA, AU, DE apart from IN) with the term "How to do well" fetches a lot of relevant results, indicating that the phrase might be an acceptable usage in other geographies as well.