Sentinel Playground is “stitching” together images from different dates, so that it creates seamless image. If you go to “Effects” and click “Show dates”, you will see different dates. We do this on purpose as we want this to be simple for users. It is not most accurate though as the images might be from different dates. If you check EO Browser, you will notice that we only show single day. Again, on purpose, as EO Browser is meant for a bit more advanced set of users.
You can get such a mosaic as well if you set a longer time interval, e.g. one month of data. You should also set MAXCC=100 (cloud coverage), so that you get all images on the chosen date.
TIME parameter should be in ISO8601 format (check documentation).
I am not sure, which time period you want to set, but 2019-3-1 is IMHO not in line with the standard. E.g. if you want to get imagery from 3rd of January 2019 to 31st of January 2019, you should set TIME=2019-01-03/2019-01-31
Second and third link are almost certainly on the border of the orbit so you will have to set a longer time period in TIME parameter if you want to get filled image.