I also found the Star TSP800 is very difficult to configure, with poor documentation. However, I was eventually able to configure the printer to solve all the problems you mentioned, except #1.
The Rx paper for this printer requires timing marks on the back (black bands at the top & bottom of each prescription). If you don't have these, return the paper and get the right rolls.
On Windows 7, open "Devices & Printers" in the Start Menu, and right click on the Star TSP800, choosing "printer properties". You need to set up 3 areas for correct printing and Rx cutoff:
1. Click on the "General" tab at the top left, then the "Preferences" button at the bottom. In the window that opens, click the "Paper Quality" tab at the top, and then the "Advanced" button on the lower right. Under "Paper Size", choose 104 x 200 mm or 104 x receipt (it didn't matter which when I set it up). Click "OK" to close the window, then "Apply" in the next window, and then "Okay" to close the window. You should be back at the "Properties" window again.
2. Click the "Advanced" tab at the top of the "Properties" window, and then "Printing Defaults" at the lower left. Click "Paper Quality" tab at the top, and then the "Advanced" button on the lower right. Under "Paper Size", choose 104 x 200 mm or 104 x receipt. Click "OK" to close the window, then "Apply" in the next window, and then "Okay" to close the window. You should be back at the "Properties" window again.
3. Click the "Device Settings" tab at the top of the "Properties" window. Change the follow settings:
-- "Form to Tray Assignment: FRICTION:" ----> 104 x 120 or 104 x receipt, whichever you chose in the two setups above.
-- "Paper Type" ----> "Black Mark".
-- "Black Mark Detect on Power On" ----> "Enable".
-- "Page Cut Type" ----> "Full Cut"
-- "Document Cut Type" ----> "Full Cut"
Click "Apply" then "Okay" to close the "Properties" window. Power cycle the TSP800 by turning it off and then on. The status light should turn green, and the printer should advance the paper roll to the first black timing mark, and cut it off.
Also, remember that you must choose the printing profile for the TSP800 in the "Set Presciption Format" area under "Administrator Options" in Amazing Charts.