A confusion on DC operating point in SPICE
I would first: short all the inductors and open all the capacitors.
  But this seems wrong. What am I doing wrong here?


SPICE is a numerical simulator. There is a rounding error in every SPICE result. 

In particular, SPICE only tries to solve the node equations until the currents balance to within an error defined by the parameter ABSTOL. In LTSpice the default value of ABSTOL is 1 pA, so if the currents at any node balance to within 1 pA, LTSpice considers that "good enough". You can change the value of ABSTOL using a .OPTIONS directive.

The errors you see are on the order of 1 pA, so this is expected behavior.


  In LTspice if we do not skip the initial operating point solution [when doing a transient analysis] and obtain results, is that equivalent to: we first do a DC operating point analysis and we set uic for each component and do a transient analysis?


Yes, this is equivalent.