- What is the difference between a human player of approximately 1600
ELO rating and a competent chess engine like Stockfish 7 set to ELO
The main difference is in the way each chooses their moves.
The human player will predominantly use pattern recognition combined with some form of plan recall. So, I recognize that this position is winning for white and this is the winning plan. This might involve specific moves for a tactical plan and more general aims for a strategic one.
The computer will predominantly use brute force calculation with an element of pattern recognition for position evaluation
- Is it possible to determine the ratings of players with the pgns of their games?
In theory, yes. Both FIDE and certain online chess providers have looked at tools for detecting cheating which essentially do this although without producing a rating. They look at moves which are not opening book / standard theory moves and calculate the percentage of moves which are engine 1st, 2nd, 3rd choices etc. In principle this work could be extended to develop a way of rating pgns but it would be a lot of hard work.
I'd play with the computer and wanted to know what is my ELO. Is it
possible through Fritz or any software?
No. Too much work to develop such a system for too little reward.
- Is there any site that explains what is ELO in lucid terms?
Since you appear to know what ELO is (an internationally recognized rating system) presumably what you are really asking is whether there exist explanations for the mathematics and statistics behind ELO.
The killer part of your question is "in lucid terms". Of course such explanations exist which are lucid for mathematical and statistical experts but just as clearly if you lack the expertise they will not be lucid for you.