Is expiation obligatory for invalidating the fast by looking at a girl and playing with the penis until semen is discharged, and is it permissible to complete the fast of that day then make it up after Ramadan?

Speaking with a non-mahram woman without a dire need is dangerous; it is a gateway to fitna (temptation/discord) and a means to corruption, and scholars have ruled it to be forbidden.

As for fasting, if what was discharged from you was maniyy (seminal fluid) due to your touching your private parts, then your fast is invalidated, and you must make up for it. If what was discharged from you was madhiy (pre-seminal fluid), then the fatwa we hold is that imdhāʾ (discharge of madhiy) does not invalidate the fast.

What is obligatory upon you is to repent to Allah Almighty.