It won't hurt the OD do use it frequently, but if you do, you may want to incorporate Randall's suggested diode to the relay. The diode will kill the voltage spike from the solenoid when disengaging the OD, and keep from burning the relay contacts. A search will bring up several threads Randall described how to install the diode.
In answer to question above, "yes", if you are in OD 2nd and shift to 3rd, you will end up in OD 3rd. But...the OD will actually cycle during the shift. In other words, as you move the shifter through neutral, the switches will cut out the OD, and then re-engage it as the 3rd switch makes contact. While that is not bad, it needlessly cycles the OD.
OD is mostly for mileage in 4th gear. That said, the racers learned to use it as "extra" gears. That is why it was originally only switched to work in 4th gear (mileage), but later switched to work in 2, 3 and 4th gears. To use it as extra gears, you would start in 1st straight. Then shift to 2nd, and then 2nd OD. Next, shift to 3rd while clicking off the OD, so you go to straight 3rd...and then OD 3rd. Same to 4th. Click the OD off as you shift to 4th and go into 4th straight...and finally to 4th OD.
Personally, I don't need that many gears, as the Triumph engine is plenty torquey to work through the straight gears, and then add 4th OD to get better mileage and less engine whine on the freeway. You can use the OD anytime...uphill, downhill, etc. It will not hurt the OD.