In a screen with a table, I created a new pushbutton. When the user clicks on this button, I want to read a value from a selected table line, and pass this value to a new transaction. This new transaction has to be started in a new mode, together with an InputScript. Is this possible?
Yes, this is possible, but a little bit tricky:

Your pushbutton starts a first script, e.g. "s1.txt", without a function code:

Pushbutton (...) "some text" process="s1.txt"

At the beginning of "s1.txt", before the first Screen command, you determine the selected table line and set the cell value into your own variable, e.g. into V[selvalue]. Then, after a "Screen" command for the current screen, you use an Enter command to start the new transaction, passing the value to the InputScript "s2.txt":

Screen ...
Enter "/Oxxxx" process="s2.txt"
using p1 = "&V[selvalue]"