The meter I have I believe is a old version. So there are some small changes.
There is a oscillator made of a L and C + op-amp. There must be a L and a C all the time. When measuring parts that are very small the L or C approach zero. The oscillator will not work work with zero parts....so.....with no part connected we have a 82uH and 1000pF in the oscillator and it works fine. (is is calibrated to be "0") If the L to be measured is 1uH the total is 83uH and 1000pF. The frequency of oscillation if measured and subtracted from the "0" frequency. Through math we know the inductor you added. (a 1uH and 1000pF will not oscillate)
1) Yes the L unknown is in series with the 82uH.
2) The unknown cap is in parallel with the 1000pF.
3) I don't know. (don't remember) My bad memory says my second cap is much larger.??????