I don’t know why the AP flown this ILS above Glideslope. In the 3. screenshot I was flying manually and tried to fight against the turbulences and to catch the GS. There is still a lot of space for improvement for my manual ILS approaches with the Airbus.
And yeah, the FD shows a lot of strange directions inflight.
Anyhow, the ILS 28C worked and the OP got some issues as a pilot and it’s not a sim bug with 28C.
So, after retrying both the stock B747 and stock A320, I can confirm the issue is the sim is not loading the correct ILS frequency for 28C. Instead it loads the ILS for 28R, despite me creating the flight plan from the World Map with ILS 28C approach.
Since it affects both aircraft, I assume this is just one of those many fundamental bugs that makes relatively new sim pilots like myself unnecessarily frustrated! Now I can go back and work on technique until I find the next bug that makes me pull out my hair.
Thanks for all the tips and suggestions above.
Happy to report not pilot error, but sim bug that made me think I was going crazy!
Now, back to all my other piloting errors 
I had no problem loading the correct approach from the world map. That’s not to say that this doesn’t happen. You’re right that this occasionally does happen. I was just unable to reproduce the issues in this instance.
However, another thing to keep in mind is the role of the flight crew in managing the automation in a large aircraft. The pilots need to ensure that the plane is set up for and configured for the route that they are cleared.
I suggest that you validate that the correct procedure is set up in the FMS as the approach gets assigned by the controller. Although the flying community, especially airline dispatch offices, are fairly good at requesting and predicting runway assignments in flight planning/pre-departure clearance, operational needs and weather in the national airspace do change runway assignment. We should always be ready to receive new clearance and/or validate set up.
In this case, yes, the sim probably loaded the wrong runway, but that’s something a crew would have corrected/looked at when validating the flight plan prior to push and again as the runway assignment came in on descent.
In real life, one of the biggest difficulties student pilots have when training for instrument rating is staying ahead of the plane - making sure the plane is set up to fly the route before it needs to fly the segment ahead.
Good luck! 
EDIT: I mean this only to offer some additional realism going forward, as you start to develop your own mental checklists of what to do and when.
Yes, managing speed and altitude while traversing the waypoints and getting ahead as you state is something that still needs more work on my end. Often times I’m not descending quickly enough while also being too fast. Not a good combo.
This is an actual sim bug! TOD (top of descent) clearance comes wayyyyy too late.
Good rule of thumb: Distance x 3 = Altitude e.g. 100NM x 3 = 30000ft
Crosscheck every 10NM and adjust the rate of descent accordingly.
ROD = groundspeed x5. E.g. 400kts = 2000ft/min.
Good to hear that is not only a pilot error. 
As anytime in Aircraft related incidents and accidents, there is a chain of failures coming together.
In your case, first failure was a sim bug which occured at your destination.
Second one, as @trex5365 already mentioned, was a pilots error, because you’re not checked the approach related facts. 
Anyhow, you learned something and in opposite to real life, nothing happend and no one hurts, so you still can have fun with the sim.
I would be completely fine with an “intentional error” feature where occasionally info gets transcoded incorrectly or entered with a typo. You could turn it on/off based on your comfort and familiarity with the aircraft.
I’m not as ok with a bug that got me four times in a row that we just write off as a “realism” feature. I think we’re letting Asobo off too easily if we think that, however that topic has been beaten to death in every other bug thread, so I probably shouldn’t be beating that dead horse any further.
I think you’re right here.
When there are multiple bigger bugs in the sim, I don’t think this topic gets a lot of attention because most have in their flight deck flows to set, check and validate. We’ve gotten used to going through the corrections as required.
But yes, it should “just work.”
It’s not realistic. This doesn’t happen IRL. It’s apparently a very basic bug.
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