To show the individual points that you plotted with Farm Site Mobile, when you import the file into Farm Site be sure that the "Import as Lines" option is turned off in the Import box. This will give you a point for each logged point.
If you want both the lines and the points displayed then import the same file twice, once with the "Import as Lines" option on and a second time with the option off.
With regards to suspending the recording of information in Farm Site Mobile, select the "Stop Log" option at the end of one "run" then select "Start Log" and enter a new file name when you restart the next "pass". You will need to use a new file name for each "pass" (if you use the same file name you will lose previously saved data).
With regards to the program continuously recording information when you are logging single points, if you import the data as lines, Farm Site will draw lines between all points being imported. If you import as points, no lines will be drawn and you will see each point that was logged. If you are logging some areas continously (such as to log boundaries) and you are logging some individual points, then I would recomend Stopping the log at the end of the continous data and then Start a new log to log individual points.
Please let me know if you have any further questions.