my first post here. Link to video of the problem down below.

We have a problem with our toilet. When we flush it, water rises in the pot, then slowly leaks away through the drainage pipe on to the floor (with bits of excrements in it). I took a video of the problem to possibly send to a plumber. However, firstly i wanted to know if it is possible to fix it ourselves.

The water seems to be leaking through cracks in the foam/paste(?) where the drainage pipe goes into the floor. I was wondering if unclogging the toilet and re-applying the foam/paste would solve the problem, or if it would only serve as a temporary bandaid. We haven't tried this yet because: 

1. We currently don't have a plunger.

2. We don't want to worsen the problem incase a plumber needs to come

All help is welcome and thanks in advance!
video of the problem: https://i.sstatic.net/pLlaM.jpg