My question on this meter is: Once you set the forward position, (1) Does this "set" position give you an accurate SWR reading in the reflected position.
It should, as long as you don't change the band or power level. (If you do, you have to
readjust the "set" control.)
That assumes the meter is properly working. Many of the inexpensive SWR meters are quite
frequency sensitive: I have one that takes 25W to reach full scale on 80m, but only about
20 milliwatts on 2m. Unless the meter or the diodes have been burned out (certainly known
to happen when too much power is run in the low power position) then one or the other
setting might not be functional.
The meter might also not be adjusted correctly: to check, measure the SWR then reverse
the meter connections. Set the meter to REV, adjust the "set" control to full scale, switch
back to FWD, and see if you get the same SWR reading you did the other direction.
(That doesn't guarantee it is working, but should give about 90% confidence.)
Note that meters do have a frequency range outside of which they lose accuracy. I've used
the cheap CB meters on 80m through 2m with reasonable results, but couldn't generate
enough power to get a useful reading on 160m unless the antenna was already matched,
and the readings were totally bogus on 440.
(2) If your SWR is high, adjust the antenna to get it as good as possible, then when it is good , do you then just remove the meter and hook the antenna directly to the radio?
You can take it out of the line if you want, but you don't have to. On HF I usually leave a meter
in the line to monitor my SWR, especially when I am using a tuner. On VHF I usually remove it,
as my antennas usually are more reliable.