You test resistors with an ohmmeter. Reading in circuit can give questionable results, as ther can be non-obvious conduction paths which will result in low readings. Always make sure the circuit is deenergized first. Having devices like ez-hooks rather than the normal probes makes life easier.
Learn the color code, too. It helps if you know in advance what the resistance should be.
Yes there is, just pull out one leg then you dont have to remove it completely from the board haha, just kiddin. But you can do it this way for axial components. With chip resistors in surface mount implementation, you cnat do it this way
It will be very difficult to check the actual resistance of a resistor in circuit, specially if you dont know how it was connected within the schematic of the board. And even if you have schematic, it's difficult to do, i.e. you have a resistor to test that based on the schematic it is parallel with another resistor, though you may be able to analyze and get a calculated estimate on how much resistance you would expect to read including the surrounding component that may influence the reading.
Also another way you can do when doing some test in circuit, is to conduct voltage or current measurements. For transistor based circuits, voltage reading is very effective specially when checking the bias voltages from point to point. In this way, you can avoid doing resistance check by having some conclusions based on your voltage readings.