The officially named "Questions to the Prime Minister" is also known as "Prime Minister's Question Time" or just "Prime Minister's Questions," and then simply PMQs. I suppose we can take our pick on what we want to call it.
As for the political parties switching and sitting on different sides of the House, that's because the party that is voted into power after a General Election always sits to the right of the Speaker. The opposition parties sit to the left of the Speaker.
There can be around 8 different political parties sitting on the opposition side. The party that has gained the most seats in the General Election becomes His Majesty's Government, whereas the party that has gained the second most seats, but did not achieve a majority in the General Election, becomes His Majesty's Loyal Opposition.
The main role of the 'Opposition' is to scrutinise and to hold the government accountable.
I can vaguely remember the news reporting that George W. Bush had said he wouldn't want to go head to head with the opposition in a debating chamber the way a British Prime Minister does, or something along those lines?
It doesn't really matter which party is in power, they all get similar treatment from the opposition. Brace yourslves, Prime Ministers Question Time: