How to determine the screw size (No.)

Michael said many good things in that response. Read it. As an addendum....

In most cases, if it feels loose, then use a larger driver. A screwdriver should fit snuggly in the recess of the screw you are driving, without taking force to inset the bit into the screw. If it does not, then you are using the wrong one. It should have a shape that matches. Do not use something with only approximately the right shape, and jam it in. Thus, do not jam an Allen head bit into a Torx screw. This means you must know what kind of screw it is. If you don't/can't recognize the type of screw, then don't try to turn it.

There are some screws that are a combination head. For example, some have a doubly slotted head that will take a Phillips driver, but also a square recess for a Robertson driver. In that case, use a square (Robertson) drive. It will be a better fit, and is far less likely to slip and cam out. Even better is to use a driver that is designed to fit into that style of screw, with a shape that completely fills the recess to yield the highest torque.

For a flat head screw, again just use the largest driver that will fit snuggly into the slot. This will offer the greatest amount of leverage and thus drive the screw with the greatest torque for the largest turning power. Since large screws with large slots may require a large amount of force to drive and remove, this just seems like common sense.

I think the bits as basically very low quality. When you go to your favorite store, simply buy one of the contractor grade of bits like DeWalt, Kolbalt, Irwin, Vermont American etc. Be careful what kind of jobs you tackle with your light duty screwdriver. I'm sure it does not have the power to drive longer screws into hard woods like decking etc. You have to hold a lot of force against the screw in these situations or the bit will slip, spin and dull, as well as strip out the screw head.