How to answer questions about Latitude and Longitude in Spectrum Spatial Analyst

Which projection is used in Spectrum Spatial Analyst(SSA) for entering Longitude and Latitude in the search box?

If the Base Map doesn't support Longitude/Latitude then SSA converts Longitude/Latitude to X/Y by assuming that the user is entering Longitude/Latitude in EPSG:4326 projection. In the case where the map projection is in BNG (EPSG:27700 ), and Longitude/Latitude is being entered in the "Enter coordinates" section, then SSA assumes that the coordinates being entered are in the EPSG:4326 projection.

Do coordinates have to be entered in the decimal version or is it possible to enter degrees, minutes and seconds?

It's currently not possible to enter degrees, minutes and seconds, as SSA only supports the decimal version.

In the user guide it says that the Longitude and Latitude can be included in a callout, however only the Eastings and Northings are showing for BNG. Is it possible to make a call-out show both Eastings/Northings and Longitude/Latitude?

It is possible to see both Eastings/Northings and Longitude/Latitude on the call-out in the SSA 12.1 release:

New feature : Current Coordinates : Users can view the coordinates of the current map center and the map’s extents in both X-Y co-ordinates of the map projection and in Longitude-latitude. The Administrator can use this feature to setup the initial map center and pan able extents for a map configuration. This option is available from Right hand panel > Options tab.
Environment Details
Products affected: SSA
UPDATED:  November 30, 2017