Is the vibration only on acceleration or can you feel it when cruising/coasting as well?
Acceleration could be CV axles unbalanced, or many other small things like mounts, control arms etc. I would have it inspected and eliminate the small things before jumping into deeper diagnosis.
Other items could be bad tires (out of round) or simply unbalanced wheels.
As for oil, keep using 5w30 regardless of your engines Kms. You 'can' use those expensive brands. I personally would be fine with a locally packed brand like total or shell. Ensure you are buying whatever oil from a reputable source as there's lots of fake in the market.
As for level, if you have the owners manual, that should tell you the correct amount. Otherwise, after an oil change, have the tech till 3.7, start it, check the dipstick. Add as necessary.
If your car feels a bit sluggish, it may be time for some generally maintenance. Air filter, spark plugs etc. Good time to have the transmission fluid done (auto) if not already.
I believe @dani_kk has a shop in your area if you need a good mechanic. Have heard good things about him on this forum.