This might not be the answer, but for reference here is a problem that can occur if the plumbing is not installed properly.
If you look at Fig. 3, this is what a proper drain looks like. You'll notice the orange line represents the water level in the system, the water levels out in the trap preventing sewer gases from entering the sink drain.
In Fig. 1, you can see what will happen if the drain line has to go up before meeting the main drain line. Again the orange line represents the water level in the system, and as you can see the water level is much higher in the drain.
Fig. 2 shows what could happen if the sink was installed lower than the rise in the drain line. The water would never fully drain from the sink, since it would require extra pressure in the system to push the water up the drain.
![enter image description here](https://i.stack.imgur.com/Ws9y4.png)
I wouldn't guess this is the issue in this case; since as you can see, if you opened the trap in this case you would have more water drain than what is typically in the trap.
In a perfect world Fig.1 and 2 would never pass inspection, but as we all know not all plumbing is properly installed and/or inspected. So this could possibly be the case in this situation (given the plumbing was installed by an amateur plumber), but it is doubtful. It would be more likely caused by a clog in the line.
It appears from the video the sink bottom connection is assembled wrong. From top to bottom you should have sink, rubber gasket, metal flat washer, brass nut. This or the P-trap connection do not need to be super tight, firmly snug should be enough. If the connections leak when snug, the gasket or sealing ring is likely damaged, or possibly their mating surfaces are not clean and smooth.
More disturbing is you say drain/popup detached from the sink when you were fussing with the P-trap? This should not be possible. If it did happen, the drain/popup is broken and needs to be replaced. This is not something you could have done alone, it was ready to break anyway. The flange you see when standing over the sink is part of this assembly, the large nut underneath sort of clamps the sink between the rubber gasket and this flange. The drain/popup is normally installed by dropping it in from above. If it came out from the bottom it is broken.
Best Answer
Read the Safety Data Sheet! You've used a very hazardous chemical, which reacts with water to get very hot. It can easily get hot enough to boil the water in the drain, causing the boiling hot caustic (able to dissolve flesh) solution to spurt out the drain, perhaps onto you! It can also get hot enough to damage pipes, particularly those of plastic, and it could then leak out into a cabinet or onto the floor.
Do NOT touch any spilled crystals or leaked liquid. If you have, wash where it touched with a lot of vinegar.
The crystals have clumped in the drain, and perhaps the best thing to do would be to fill the sink with cold water and let them dissolve, which they will do over time. Do not push anything into the drain to speed this up. If this doesn't help, call a plumber, and warn her or him what you put in the drain.