First, congratulations on facing your fear of flying.
What you saw was nothing out of the ordinary (also, asking the crew things does not make you end up on terrorism watchlists).
From a passenger perspective, it's extremely difficult to judge your whereabouts. Taxiways and runways are difficult to distinguish, especially because your forward view is limited. The layout at Budapest, with runways far apart, does not help. Long taxiways may look like runways (taxiways may be very broad) unless you know exactly what you're looking for. I've invariably completely misjudged my position on the airfield as a passenger despite using the hours before boarding checking out the airfield layout.
Furthermore, the crew may elect to use a higher taxi speed on long taxiways, so when braking for a turn you suddenly realize how fast you were going. However, compared to the size of the plane this is still quite slow. Think of the feeling you experience braking for a bus compared to what you felt in the plane - a plane will taxi at what would be a fairly high speed for a bus. Due to the size of a plane and lack of external reference, cornering may feel exaggerated with respect to reality too - a 90 degree turn may feel like a 180.
Finally, the flaps are configured during taxi, no need to be stationary. This may be done in steps (a little bit before taxi, some more during) Controls can also be tested during taxi (full deflections to all sides). This is completely normal.
So, what you experienced as a sequence of things that are completely normal but feel very different inside the airplane than the way it looks on the outside.