You must be flying after 1st April 2014 - APD will for non-cheapest cabin in that distance band will rise from £166 to £170.
Anyway, your questions:
Passenger Service Charges increases from £12.27 to £29.99 when both EDI and LGW are utilized. Do we pay the Passenger Service Charge for each UK airport we use on any one booking? It seems funny that adding EDI brings it up to exactly £29.99.
Normally, yes - subject to some provisions where you sometimes play less, more or differently as a connecting passenger, in some circumstances. But I would expect to normally.
However I would expect £12.89 plus £9.67.
Perhaps they are including something else with this?
Rounding up what looks like marking prcies (29.99) is not unheard of, with odd figures it happens a lot.
Air Passenger Duty rises from £170 to £183 when adding a stopover. I presume this is because each flight is rated individually and this is the total (£13 is the surcharge on an EDI-LGW)
With a stopover you have exceeded the permitted time for it to be considered a connection, therefore you pay a shortest band (single class) level APD for flight 1 £13, in addition to the APD for UK to Mauritius.
When UK connecting or single sector it would just be a UK to Mauritius APD.
If connecting from non-UK, zero UK APD.
Fuel Surcharge rises from £359 to £396 when adding EDI-LGW leg. Is this normal?
To be expected.
Assuming this is a redemption, if you are not connecting and don't need the protection, and also don't need the higher baggage allowance from your later flight, you might find it better value to book the EDI-LGW as a Reward Flight Saver at those rates.