Alternative equipment(s) to drill a few holes on a 0.5 cm plastic beside using a small drill

You can absolutely do this yourself with a powerdrill and 21 dollar diamond hole saw from HD. For a standard faucet hole, you need a 1 3/8" diamond hole saw. I ended up not only drilling the faucet hole, but laminated the edge to double the thickness, polished with a diamond pad, and installed an undermount sink. There is no doubt that this is a risky DIY project if you don't research how to do it properly. But I learned through online videos and resources, then practiced on the excess portion of the slab. If you would like to see what I did, search for "Thrifty Tani" on youtube. I shared my experience my videos. He'res a link to the videos How to drill a faucet hole: https://www.youtube.com/watch?v=bFWvVzlGF4Y&t=5s

If you are set on using a hand-drill, there are jigs available that will keep the drill perpendicular to the object being drilled. Alternatively, holding a level against the drill will help you keep it aligned.

I would suggest using a Forstner bit instead of a spade bit. Spade bits can jump around a bit, tear out and are not that precise. They are good for rough work, but a Forstner bit will give you a much cleaner cut.

That being said, a drill press is the best tool for this, and they can be purchased relatively inexpensively. You could also find a "maker" workshop in your area, or a college with a shop where often you can rent time and use their tools.