Hi Nick,
I think Polish girls are not that open-minded as American girls as far as dating is concerned. While for an American going on a date with one guy one weekend and with another the next weekend is "normal", Polish girls are more careful which guy to choose. In result, you are right when you say that she wants you to wait a little longer -- probably she just wants to get to know you better. The fact that she rejected other guys confirms that.
It's good you made her laugh and even better you try to speak some Polish

.
When it comes to relationship, no "magic phrases" exist, I'm afraid :|. You could try "I like you" - "Lubie Cie" though. For other basic phrases you may check www.polish-dictionary.com.
Keep trying but do not rush it.
Best,
andy