Hi Rebecca,
These are few reasons why label might fail:
1) SSA 12.0 had this bug - Consider a map with many layers. SSA connect page loads with this map, but map is set to be 'initially not visible'. Then user switches ON only one of the layers (instead of ticking the entire map ON). Notice that labels are missing. This is fixed in 12.1.
2) In 12.1 (and older SSA also), if a map has the same layer added twice labels don't seem to work. i.e If MapInfo user has added the same tab file twice into the workspace and then uploaded into SSA, it seems to affect labels.
3) Some label setting in MapInfo are not supported in SSA
-Curved labels are not supported. Release notes states this.
-For Label expression, "Functions" are not supported and Map Uploader gives a warning in 12.1
-Applying "Try other positions" for map labels in MapInfo causes SSA labels to fail sometimes.
If none of above, please check the browser dev window (opened by F12 key on browser) for SSA mobile page. Are there any errors?
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The first issue you have reported fits the symptoms of labels bug in SSA 12.0 - "the only way I can get labels to display for a layer that is a part of a map group to display, is to turn on ALL of the layers in that group" . It will resolve once your installation is upgraded.
For the second one, please email the workspace containing the Roads layer for testing to PB support.