1st problem could be a number of things - throttle position sensor, gearbox electronics, etc, etc. - best bet would be to go and get the fault codes read out by a specialist (shouldn't take more than 30 mins of a garage's time - most have diagnostics nowadays). If you act like you want to get the car repaired there, they'll not charge you either! I would suspect something electronic rather than mechanical.
Second prob could be wheel bearing, or a wheel out of balance (check the alloy to see if it's got a flat spot), or the wheel not tightemed properly (worth checking quickly!). Could also be a tyre fouling the arch if it's got stupid size wheels on!
Good news is if the engine is smooth under normal operation, it's nothing terminal!