I just completed a trip and went from no status to crystal and sapphire based on the calculation.
How long before I will see my status reflect?
Will I receive both the crystal card and sapphire card or just the latter?
What about Global Club invitation/registration?
The status will change as soon as the flights post. As I guess there will be a few flights and thus days between Crystal and Sapphire, they will send a card each time you reach a mile stone.
Once you reach Sapphire, the JGC invitation arrives as well. If you are Japan based, pending you have a credit card as well.