Transition altitude will generally depend on country, eg USA is 18000 but UK is 6000 but individual airports can have a different figure depending on terrain.
The rest are all runway dependant and although the majority of airports will have identical or very similar numbers for each runway there can be significant differences, again mainly dependant on terrain during the approach/missed approach procedure. The only way to check for sure is to use the charts.
Unfortunately charts are you best source. Principally because airports will often have their own transition altitudes as well. For your Final Approach Altitude that will be the intercept altitude with the glide slope and will be identified in the ILS charts.
In ICAO there is a slight difference regarding FAF. Apart from it being termed FAP "Final Approach Point". So the FAP distance is the distance at which you are expected to intercept the glideslope. Currently PF3 has set 7nm as the default value. This translates to 10-11nm from the threshold in the sim if the glideslope is 3deg. and your approach is 3,000ft agl. So for a large majority of airports it doesn't need to be changed. But you do need to check first.
Bear in mind also that FAF/FAP altitude is QNH and not height above ground. So in this chart below you see 4,000ft as the FAF altitude which in the case of Torino is 3,000agl. The numbers on the scale with "D" in front refer to DME
NOT GPS. DME on an ILS facility is measured from the ILS localier which is at the opposite end of the rwy to your landing so it will disagree with your GPS by at least 1nm!
If you fly in Europe our best source is Eurocontrol as all European nations must file changes and updates with them. You will have to register though.
Another point to consider is your afcad file. They quite often disagree with the real charts so may need updating. Flight planning does unfortunately require a little work
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