I also just re-watched episodes 601-612 (last Friday/Saturday) and truly enjoyed them better than I had recalled, but especially the first 6. I think the Season 5 cliffhanger left me anticipating too much, so when I first watched Season 6 eps, I felt fairly unfulfilled. But on a pure entertainment level, I have few complaints.
If I understand the series vs. season question ... in the US, the show in its entirety is called a series. The individual years within the series are called seasons, because we have a (crazy, wacko) television industry that operates by a "viewing season," which follows the school year, Sep-May (used to be June - also, used to begin earlier in Sep, I think), and is distinguished by numerous, annoying breaks in original programming and peak periods during which everything you might want to watch is on at exactly the same time.
Most episodes of Friends are rated PG, some are rated for older audiences because of content (usually, frank sexual discussion rather than the usual innuendo). Here, those episodes are rated TV-14, and we see this as a rating on the TV, even though we don't get the videos. Has anyone noticed that many TV-14 episodes have become PG when they hit syndication? I keep track of these things, because I don't let my kids watch the older-rated shows.