Standard slot drills and end mills are ground with the ends slightly concave, about 2* if memory serves. The intent is to provide relief so only the periphery of the tool engages the bottom of a slot. If you need a dead flat bottom the tool needs to be re-ground. When plunging I find the 3 or 4 flute end mills are more stable than the 2 flute.
Most 2 flute cutters will be center cutting. Not all cutters with 3 or more flutes are center cutting. The vendor should state if it is center cutting.
In re-grinding some of my own cutters I do not always try to re-establish the center cutting configuration.
The concave end of end mills does nothing to keep them on line. You depend on the rigidity of your machine and your part clamping to hold to keep the cutter on line. Starting with a smaller slot drill should help by reducing cutting forces.