Besides gdal2tiles, you could use vips. Details are in here: https://stackoverflow.com/a/51852934/10168903
If you want a GUI based solution, you could use Photoshop or Microsoft Image Composite Editor. You would need a plugin from zoomable.ca though.
Yep looks good.
Geoserver is probably a bit more mature than QGIS server and may give you a bit more robustness and flexibility for scaling/load balancing etc etc. But I haven't implemented QGIS Server at scale yet, so my opinion is a bit speculative.
Leaflet is pretty good client tool as well and is my preference over Openlayers, or others. But again - ...