What are primary and secondary research?

Primary research is research you conduct yourself such as surveys you made or maybe your asking people questions. Primary research is first hand.

Secondary research is gathering information from a third party source such as forums or research somebody has already conducted and posted for others to learn from.Secondary research is Second hand.

Two examples of primary research:
Surveys and Observations

Two examples of secondary research:
Third party websites and ratings

where could i use these research methods to analyse a problem within a game?

If there was a sound problem within a game i would play the game myself to test it and also take surveys about what people think of the audio problem these would be considered Primary research. I would then check the review and go to game forums to see what people are saying about the game and the problem/s it has this would be considered secondary research.

What is quantitative and qualitative research?

Quantitative is where a group of peoples opinion is turned to facts in other words its a majority wins vote of opinions.
Qualitative is used to gain an understanding of the opinion of the average person/s it helps delve deeper to see the problems with the (lets say audio) audio so they can be fixed so more people enjoy it.

Two examples of quantitative research?
Ratings and