If you look closely at the tip of your drill, you will see that it comes to a so-called chisel edge; the very tip is actually a short sharp line and not a point. If you are going to pick up a centre punch mark with a drill like this, you need a dimple from the punch that is at least as big as that chisel edge so that the "point" of the drill sits right inside it. One way to do this is to use a small sharp punch to put the first mark in and then go to a bigger punch to enlarge the dimple. The other way that works for me is to use small centre punch mark and then go through with a smaller drill (say, 2.5mm or so). These are a bit more fragile so need a bit of care but these smaller drills have a much finer point and they will follow the mark and go through the steel much more easily. Then follow up with the 4.2mm which should follow the pilot hole. Advice to use centre drills is great and probably the proper way to do the job, but only if you can clamp the work firmly on the drill table. The points on these things are pretty fragile and while they'll take quite a lot of downforce for cutting, they will snap at the slightest sideways movement.

I don't know if it's encouragement or not, but I drilled all the holes for my linear rails (total of about 100 M5 tapped holes) freehand using a cordless drill. However, I clamped the rail in place and then used a little drill jig to locate in each hole in turn to guide the drill so that it was central in the hole and close enough to square. I am using 3mm steel, but I have strengthened it with 5mm strip on the inside so I was effectively drilling 8mm of steel with a hand-held cordless drill.

For tapping, forget the usual hand taps. Get hold of some spiral point taps if you are tapping through holes, and spiral flute taps for blind holes. They are ground very differently to hand taps so that they can be used in tapping machines to tap a hole in one pass - no backing off every half-turn. I've used a spiral point tap in my cordless drill for tapping some of those M5 holes and (using a good tapping compound to lubricate the tap) they are magic. They are pretty cheap although you'll have to wait for delivery from China. You'll find them on eBay.