I just bought a 2006 Mazda3 with a manual tranny (first time stick driver) and it so far has been a great car barring any newbie manual mistakes. I've noticed a couple things that I am curious of whether they are normal for the car or need to be checked out.
I have noticed slight shaking/rocking when letting off and pressing down the gas. I would describe it as a forward and backward, almost bouncy motion that rocks about 2-3 times quickly, rather than a shuddering of the entire car. Even if I feather the gas it still seems to do it about half the time, and the effect is less noticeable in higher gears.
At speeds around 50mph+, 2.8k+ RPM, and when in 5th gear the entire car sometimes shakes and can be felt in the steering wheel. I only notice it in a particular section on my drive to work which is slightly uphill so I could see there being too much load for that gear, though I haven't driven on the highway at cruise enough to see a pattern.
There seems to be a low vibration/humming throughout the entire car at idle and when driving. I can feel it in my steering wheel and in the dashboard. It's not strong so no loss of control but I definitely "feel the car" more than I did in my previous one. At idle the engine has a loud hum. The RPMs do not fluctuate at idle.
Thanks in advance for your help. I am a bit of a car noob so I don't have the materials to fix anything myself though if there's anything I can do to test/diagnosis these issues I'm all ears.