Hi there!
And yes, the same thing happened to me for my undergraduate degree.
Here's how it goes:
1) You are allowed to enter the USA up to THIRTY DAYS prior to your school starting. So August 5th would be the first day you are allowed to do this.
2) If you need to take another semester of schooling, your school will extend your visa, not a problem.
3) The visa date now is the projected date upon which you will graduate. You have a "lax time" of 60 days from the day your visa expires to eave the country or go on OPT (optional practical training, an option that lets you stay in the USA for one more year, not including said 60 days, to work as long as it's related to your field of study).
Overall, no worries there. You have 60 days after you graduate to get out, you can get in the USA up to 30 days before your program begins and if you need an extra semester... your school will do it. But by "2 years" they do usually mean it the way your visa has it.
The second question I wouldn't know, sorry. I'd call your school's ISSS (International Student and Scholar Services) office and ask them about it. Usually they're very friendly people.
Oh and tip for the future: Make friends with somebody in the ISSS office. It goes a LONG way further on down the roaad, trust me on that one!
