Is it possible to catch small trout with 8 wt fly rod?

It is possible, but it is not fun because you will be really overpowering the fish; one other thing is the flies used for the small trout could be destroyed from the heavy line moving them through the air. Fly rod weights come in many sizes from 0 to 12 weight but there are lower rod weights than 0 and bigger rod sizes than 12; most situations for small trout a 3 or 4 weight might be just right but if weather conditions in area these fish are at do not get much wind, then a 2 weight would probably be great.

Possible- yes. Practical- maybe not. It really depends on the waters you are fishing in.

Yes it is certainly possible. Good luck.

As long as you use small enough flies and a light enough tippet on your leader. However, considering where you are likely to find these small trout, the length of the rod will possibly present the biggest problem.