What is the ruling on the emission of semen with desire and thought, without masturbation or feeling its discharge, and does that invalidate the fast and I'tikaf?

The fast is not invalidated by the emission of semen due to contemplation, according to the majority of scholars, nor is it invalidated by the emission of prostatic fluid (madhy) at all, according to the more preponderant opinion. Therefore, your fast and your Iʿtikāf (spiritual retreat) were not invalidated by what you mentioned, whether it was emitted before Fajr or after it. However, one should not indulge in imaginations and thoughts.