Sorcerer Questions

[Todd Que]

OK, bear with me here...I primarily play melee characters and don't do much spell work, so when I get into the rules there, I get a bit confused.
Help me out with some of the basics of Sorcerers and their spellcasting. 

So, let's take a look at a hypothetical 1st Level Sorcerer.
At 1st Level, she knows 4 0-Level spells and 2 1st-Level spells.  That means she has to choose those spells when the character is being created. 

Let's say she has the following spells:
0#1
0#2
0#3
0#4

1#1
1#2

So, how would that work in the game?  Lemme see if I'm getting this right...
At 1st Level, she can cast 3 1st Level spells per day.  Let's say she has a 17 CHA score, which would give her one more 1st Level spell per day, for a total of 4 1st Level spells per day.

She would be able to cast any of the KNOWN 0-Level spells as many times a day as she wants.  From my little list, she'd be able to cast 0#1-4 a million times a day.
She would be able to case any of the KNOWN 1-st Level spells 4 times a day.  From my little list, she'd be able to case 1#1-2 a total of four times per day.

Am I getting this right?