Yes, I tried putting Origin in Offline Mode while connected to the internet and that starts the lag problem right then and there. I've left it connected by default, but in the actual game settings themselves I've unchecked the boxes pertaining to the internet. They don't seem to have an effect on gameplay whether they're on or not from my experimenting with the settings.
But I have noticed that if I trick the game into thinking I'm connected by starting it while I'm online and then disconnecting myself from the internet, then it runs perfectly fine the entire time I play. It's when Origin isn't connected to the internet when I start the game when I experience the lag.
As for your other questions, I'll have to work on them or test them out when I get back from my vacation, because I won't be taking my laptop with me. (I might even come back and ask how to do some of them since my knowledge of computers only goes so far.) Hopefully one of those errors is the problem and will be an easy fix since I'm already pretty addicted to this game! XD
(Edit: I forgot to mention that my vacation runs from July 1st through the 10th. I'll try to check for a reply between then, but I can't make any promises. Also, thank you for taking the time to try to help me with this!)