The lady did not sleep with Renault. She was contemplating it and wrestling with the morals in her head as to whether or no she should so she could get the exit visas

It's worth noting that the film is from 1942, years before World War II ended—at a time when no one knew who would win. And many of the actors were actual refugees. No wonder they sang the French national anthem with such enthusiasm.

Guys, she did not think she was going to America with Rick, she believed Victor was going by himself, and she was staying behind with Rick.

The emblem on the ring shown to Lazlo is the Cross of Lorraine, the emblem of Free France (1940-1944), which, under de Gaulle’s leadership from London exile, opposed the Nazi takeover of northern & western France and the collaborationist Vichy government in southern France headed by Philiippe Petáin.

Early in the film, when the man whose papers have expired is shot, he is right in front of a mural depicting Petáin. Toward the end, Captain Renault tosses a bottle of Vichy water in the trash, demonstrating his belief in a free France, just before he says that Rick has become a patriot.  Rick’s shift from being uninvolved to stepping up to help the cause parallels America’s shift regarding the war.

One thing that makes this movie so powerful is that no one knew how the war would end, and yet they left it on such a hopeful note

80 years later and still the most quotable movie ever made. Btw, the actress playing Yvonne actually escaped France and her tears were very real.
All time classic!

When Ilsa was talking to drunk Rick after the flashback, she said  "She looked up to him (Victor) and worshiped him… with a feeling she supposed was love."  She was trying to explain to Rick that she admired Victor but was not in love with him.  She was in love Rick.

Current audiences often don't understand the timing of this movie.  It is set during the week before the attack on Pearl Harbor which led to America dropping its neutrality and entering the war against Germany.  The movie was released about the time US forces entered combat in North Africa, including landings on the beaches of French Morocco.

The scene where they sing the national anthem of France always makes me cry, it’s a really powerful scene of defiance against the Nazis

When Sam begins to play As Time Goes By for Ilsa, the camera lingers in a close up of her face for a very long 25 seconds. Can you imagine a shot like that from a modern filmmaker? But then, there aren't many faces like Ingrid Bergman's.

Recall when she was telling Rick when she came back to the bar: "Let me tell you a story....about a young girl who had just come from Oslo, and met a man whom she had heard about all her life, who....she admired and looked at with feelings that SHE THOUGHT WERE LOVE ...."  She was talking about her early relationship with VICTOR.  She later fell in ROMANTIC LOVE with Rick.

That is one of the best movies ever made, truly a gem.

There's a very subtle clue about Renault at the end, when he drops the bottle of water into the trash. That bottle is "Vichy" water. Vichy was French government that sided with the Germans. That was his decisive moment of choosing the side of Free France against the Nazis.

51:53 and 55:05 I think you missed the fact that Elsa said she wanted to tell Rick as soon as she found out, that  her husband Victor was still alive and she needed to stay with him in Paris, but she couldn’t because she knew Rick would have stayed in Paris with her too and  Rick would have been captured by the Nazis (Sam said he had a price on his head) So she had to make Rick think she had left him so he would leave without her.

Rick was a cool hero.  He pretended  to not give a damn to protect himself but he hated bullies like the Nazis.

When Elsa told Rick "God Bless You" at the airport she was letting Rick know that she Loves him...which was the same phrase she left on the note at the railroad station.

A classic Champagne Cocktail is a timeless drink made by placing a sugar cube in a glass, soaking it with 2 to 3 dashes of Angostura bitters, adding a 0.5 oz splash of brandy or cognac (optional), and topping it with 4 to 5 oz of chilled Champagne. Garnish with a lemon twist or orange slice.

She was worried that Rick would not leave Paris and she didn't want him to get captured or killed

The fantastic Peter Lorre.  And the indomitable Sydney Hughes Greenstreet.  Who started his acting career at 61.

Elsa didn't tell Rick about Laslo immediately because she knew he would stay behind to try and help/protect her. Rick had a bounty on his head so she knew he had to leave. Her secrecy was designed to protect Rick and keep him safe.