When you download the pro cfw, there should be a fast recovery app.
Copy the folder to PSP\GAME and launch it from the game menu.
After you're back to XMB, check system settings>about (or something like that, it's second from the bottom). If it's saying 6.39 Pro-XX, you are on cfw.
Then you can proceed to install infinity.
About your date and time problem, i assume it is a battery problem. You can try borrowing a battery from your friend then check if it persists.