What it boils down to is that RF is AC, alternating current, not DC, direct current. What is a 'short' with DC may not be a short with AC. It depends on how that shorting is 'done'. Those antennas that have a coil at the base are one example if that. A coil that has a connection to 'ground' coming from one of the turns of that coil is one way of adjusting the input impedance of the antenna, making it closer to 50 ohms that the radio want's to see. If you measure the resistance between the connections to that antenna with a common ohms meter, it will show a short or continuity. That's because that ohm meter uses DC to do that measuring with. But at the frequency the antenna is designed for, and because RF is AC, that 'short' isn't there anymore. Confused yet? We all are to start with, don't worry about it much.
A field strength meter does what the name implies, it measure the electrical field (RF) around an antenna. They are typically a 'relative' reading meter, not 'exact' unless several other things are known and entered into a computation. Very basically, it shows that there's some amount of RF being radiated from an antenna. If you do that measuring by moving the meter around that antenna it can show you the 'shape' of that electrical/RF field. Or, if it's left in the same place while tuning an antenna it can tell you if you've found the 'spot' in that antenna tuning where you have the most RF coming from that antenna (means the antenna is tuned well, or not). If you have a very good field strength meter and know the exact distance that meter is from the antenna, you can calculate the amount of power being transmitted/radiated by that antenna. Field strength meters of that 'grade' are NOT very common at all, and the typical meter most people have can't really do that. They can tell you if something changes though, the readings go up or down from 'normal'. That can be useful.
So there you go, a very, very basic explanation of the questions you asked.
- 'Doc