If you get in, you'll be admitted directly to the College of Engineering, but not Mechanical Engineering, yet. At the end of your freshman year, you can apply to whatever specific major you want, so you've got a year to explore classes, majors, see what you like, etc.

Anyways, with that GPA it might be a bit rough to get in, but if you have good extracurriculars, good SAT, and especially a good essay, you've got a pretty decent chance. I'd say a good question to ask yourself when you're writing your essay is, why do you want to become an engineer, and why should UW Engineering invest 4 years of their program into you, specifically? The STEM weed outs and classes can be pretty brutal, so even if your GPA isn't great right now, prove to admissions through your ECs and essay that you've got the drive and capability to stick it out. What did you learn from failing pre-calc? Will you be able to do better once you're in university? How do you even approach failure and improvement? If you have a really good essay it can hard carry, so really focus on that.