No, this isn't normal. Your anchors don't fit to your screws. What is happening is that the tip of the screw reached the concrete, and, of course, you can't force a screw into concrete - not even with a drill or a electric screwdriver, and certainly not by hand.
![enter image description here](https://i.stack.imgur.com/5k7o0.jpg)
This picture shows how anchor and screw should fit into the hole. The hole definitely needs to be longer than the screw. The screw should be a bit longer than the anchor, but not as long. Maybe the clerk saw that you have picked an wood screw and gave you anchors suited for the second situation. It doesn't hurt to use wood screws with anchors in a concrete wall, you'll just have the cap jutting out a bit. But the length of the screw should be only a bit longer than that of the anchor (the surplus should equal the length of the tip + the length of the attached thing), and your cap will stick out a bit if the thing you are attaching isn't soft enough for the cap to sink in.
![hole depths](https://i.stack.imgur.com/Nwe4f.jpg)
The table shows how to determine the correct hole depth. It also tells you what diameter of anchor and drill to choose for a given screw. As for the length of the screw, it is determined by the weight it will have to carry. Vertical screws are more problematic than screws in walls, because gravity is pulling in the direction of the hole, not at 90° to it. Light curtains will be OK with your size screw, but don't put any molton on them.
The scope of your project requires an equally large scope of preparation. Swap out the ladder for a scaffold system. Replace the hand drill with, at a minimum, a drill jig to keep alignment while you drill. Use drill bits designed for drilling plastic to prevent cracking. Your emphasis on avoiding splintering/cracking increases the importance of proper drill bits. Using such a small diameter drill bit also increases the chance of snapping a bit in the hole. With a combination of scaffolds, a drill jig and proper bits, you may be able to accomplish your goal.
![representative image of drill guide](https://i.stack.imgur.com/rPo1X.jpg)
You suggest that the holes need not be perfectly straight, but a jig will enable you to drill in a safe manner to avoid snapping a bit.
A quote from a plastics web site:
Plexiglass, Lexan, Plastic Drill Bits These are the bits you need for drilling Plexiglass, Lexan polycarbonate, PETG, and other clear
plastics. The special tip design carves through the plastic (not for
use with wood or metal).
It takes a special drill bit to properly drill through Plexiglas,
Lucite, Acrylite, or Perspex acrylic sheet. Ideal for Lexan, Tuffak or
Makrolon polycarbonate sheet. Special 60 degree angle. Not recommended
for wood or metal.
These are specially ground flukes with a 90° point for drilling holes
in acrylic plastics including, Plexiglas®, Lucite® and Acrylite®
materials. Metal drill bits will not work as they are made to bite
into the metal as they are pushed into it. If they are used on
acrylics they will chip and cause other damage to the plastic.
When drilling holes for screws, you must make the hole larger than the
screw itself to allow for expansion and contraction of the material.
If not you will cause stress cracks at the hole and they will spread!
Always have a backer board behind the plastic sheet - most problems
happen when you punch through the back side. The design of these bits
helps prevent that!
Bits for cutting plastic have a shallower angle to the tip as well as less aggressive cutting edges. The one in the photo below shows it is nearly a scraping edge rather than a cutting edge:
![representative image of plastic cutting drill bit](https://i.stack.imgur.com/CSLKt.jpg)
Best Answer
If it is a steel shank drill bit, grind off where it's striped, ~2". Otherwise just skip to grinding three flats, 120 degrees apart to give the chuck something to grab. Back the bit out and start over with a nice, fresh battery. Corded drills with keyed chucks are way down in price. Using one of them could most likely get you out of this situation and would probably have avoided this in the first place.
You were using something like this, hex-headed flexible extension in a cordless, keyless-chuck drill.
When you should of been using this, 4' flexible drill bit, keyed in a corded drill's chuck with a handle.