Hi maybe someone could help me. I purchased a medium size pot for my seed and went to my dorm room and tried to put place the pot but it is still in my backpack and I cannot find a way to place this item in the dorm. Am I doing something wrong?
It's not in your backpack, it's in your Housing inventory. You should be able to pick it up just like any other housing inventory item and place it in the room (it'll turn red if it's too close to a wall or other housing item).
Yes, it counts as a housing item, which is good for Gardening as it doesn't cost pet/plant power to use.
As a side note, you might want to buy enchanted pots. A bit pricey at the beginning, but as your plants go to elder and free up the pots, you'll be ready for the higher level seeds that require enchanted soil. The seeds don't care if they don't require the enchanted soil (though they do care about pot/plot size).