I use a meter more than any other method.
1. I push it into the soil till it's as close to the bottom as I can get it, but don't force it. If it's hard to push in you may be hitting a root, so find a new spot. One or two inches from the bottom is best. It can be informative to push it in slowly to learn how the moisture changes at various levels. Near the bottom is what matters.
2. a) It's pointless to check immediately after watering. b) The meter will tell you when to water. A day or two or three after watering is when to start checking. I usually water when the meter drops below 2, but some say lower is better. When I first started using a meter, I watched the leaves to see if they were drooping and lifted the pots to "calibrate" the meter. The meter is more accurate, though.
3. I don't believe accuracy is the goal. The scale doesn't matter. Reliability is what is important. By that, I mean we want the meter to do what it does the same way every time it is used. It doesn't matter if I need to water when my meter reads a 2 and yours reads a 1 on their respective scales. It only matters that each meter tells us reliably when we need to water. We know that by learning how to read the meter relative to the needs of the plants.