1. It's 162 per team (it was 154 from about 1900 to 1962, though). Some teams don't play all 162 games, though- if a game is postponed due to rain or whatever, they will reschedule it, but if it's the end of the season and the game has no impact on the final standings, then they might just not play it.
2. In a season, the record is 116, held by the 1906 Chicago Cubs and 2001 Seattle Mariners. The Cubs were playing in the 154-game era, so while the wins are the same, the Cubs had fewer losses and thus a better winning percentage.
All-time, the leader is the San Francisco Giants, who since their start in 1883 have won 10,616 MLB regular season games. In case you're wondering, the Giants have not won the most games just because they started in 1883- there are five teams that have played more games than the Giants have, and none of them have as many wins.
3. Historically, the Giants have been good (they have the most wins ever, for one thing). In their history, they have 22 National League Pennants, tied for most in the National League (the Dodgers and Cardinals also have 22); 22 is the most pennants won by any team not called the New York Yankees. Now, a lot of those pennants (and five of their seven World Series Championships) were won while they were in New York City; but they still 'count,' and the Giants have retired numbers for players from their New York days.
There are 55 players and 11 managers in the Hall of Fame who played for the Giants at some point, giving them the most Hall of Famers of any team. The Giants have 23 players who were inducted 'as Giants' (meaning their greatest contribution was as a Giant), again more than any other team.
Only five of those inducted 'as Giants' played for the Giants in San Francisco, but that's still better for that time span than a lot of other teams.
4. From what I understand, there will now be interleague games pretty much everyday, somewhere. The Giants will play 20 total interleague games, spread throughout the season.