Can I use QGIS to access data delivered using ArcGIS Server?
The following servers don't seem to be compatible with QGIS
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As of QGIS 2.16, ArcGIS MapServers and FeatureServers are natively supported. The icons are stacked with the Add WMS and Add WFS icons, respectively.
As of autumn 2015, there is a plugin to connect to the ArcGIS proprietary feature protocol, called the ArcGIS REST API Connector. It's available in the main plugin repository, marked as experimental, with source code at the link I provided.
As long as the ArcGIS for Server map services have been exposed as a WMS (which is a matter of its administrator ticking a checkbox) then you will be able to add them as WMS layers to QGIS.
The second service URL that you provided looks like it comes from ArcGIS for Server but neither looks like a WMS. I recommend you contact their providers and request a WMS service URL. Hopefully, this may be a simple request for them to fulfil.