If you struggle, it'll be a struggle everyday once you get into one of those corporations.
Listen to yourself.
Listen to yourself.
I think that 99% of the interview questions are overkill and don't reflect the actual demands of the job, or the metrics by which you'll be measured. If you're a hard worker, a team player, and write decent code, you'll probably be fine once you get your foot in the door.
And yes, having Google on your resume opens doors.
Answering interview questions correctly within a short time frame is the hardest part - actual work is way easier for the most part.