Is this really called Laganside Courthouse, tagging house on to the end of names is something I would expect in the Southern US, not Belfast.

Micro Focus Ltd.

This is now a derelict building to be knocked down to make way for Student Housing associated with The Queen's University of Belfast

Building has now been renamed to...

Meadow House

Now called Meadow House

Unable to answer "Is this still here?" – Albertbridge Road Gospel Hall (Christian Church) – way/162272659 via StreetComplete 60.1:

Kingdom Harvest Church

Attached photo(s):
https://streetcomplete.app/p/259809.jpg

Due to close on 21st March 2025 per BBC website 7 March 2025.

The place has gone or never existed. A user of Organic Maps application has reported that the POI was visible on the map (see snapshot date below), but was not found on the ground.
OSM snapshot date: 2023-11-13T21:29:23Z
POI name: Coiffure
POI types: shop-hairdresser
#organicmaps ios

In context of overlay "Addresses" – house number 38: House – way/523320165 via StreetComplete 60.3:

House doesn't exist 36 is a block next to it with 8 houses next to it. Not 9

"Speed limit needs adjusting from 60mph to 40mph as new residential dwellings have pushed the existing 40-60mph boundary further up the road. Organic maps displays 60mph in this vicinity."
OSM snapshot date: 2025-05-11T16:17:16Z
POI name: Ballygowan Road
POI types: psurface-paved_good highway-primary
#organicmaps android