In my experience, the memorization mostly takes care of itself during on-book rehearsals. The rehearsals are more about testing out different objectives and actions, and maybe figuring out some blocking. Usually you can keep refining things well past the point that you’ve memorized the text.
No they aren’t.
Okay, some of them are.
But your grand sweeping statement implying EVERY TV show is shot out of order is wrong.
Sitcoms are usually shot in order and over the course of a couple of hours, because they are shot on a soundstage in front of an audience.
A show shot on location like Scrubs or MASH will take a few days to shoot an episode and they may be shooting several episodes at once, at least early in the shooting season, when they have a backlog of finished scripts.
As far as memorization, there are different methods. Some actors write down all their lines. Johnny C. McGinley does that and then videotapes himself reading his lines and watches that as well as running lines.
With sitcom’s the problem is that often some of the writers will bet on set on the day of the episode taping and they will often still be writing and re-writing jokes and lines.
Shannon Doherty is known for being awesome at memorization, the writers on Beverly Hills 90210 were astonished that she could be handed 5 pages of new lines, glance at them once and have them down perfectly. Of course that really didn’t make up for her asshat behavior offstage. 
Some writers/directors/creators are adamant that the actors say only what they have written. Kevin Smith and Matt Weiner are the worst examples of this.
On Scrubs, Neil Flynn was so good at improvisation that when it came time for his lines the writers would occasionally have the following in the script: “Neil says something funny.”
Friday Night Lights was very interesting as they didn’t even have scenes blocked, so the actors were free to move where they wanted. They would shoot a take or two using the actual script, then a take or two with what the actors felt was the best way to convey the scene. Kyle Chandler would often cut out whole paragraphs and just use his face and hair!!! 
to convey his emotions.