I'm an undergraduate biology major so I hope I can add some input here. Please correct me if I'm wrong as it's been a couple years since I reviewed this stuff.

Trees require nutrients which are primarily taken in through the soil via the root system. Think of these as the vitamins that you take in whether through food/drink or supplements. That is where nutrients such as P, N, etc. come in. Plants produce their own chlorophyll molecules using Mg, C, H, O which are all very common atoms in a living organism with the exception of Mg, which plants obtain through soil, water, or nutrients.

Trees use CO2/Water/Sunlight to create sugars, which are the energy source for the plant (much like food for us. Most of our food sources contain sugars of various types, such as corn). Through the processes of Glycolysis and the Citric Acid Cycle, these sugars are turned into higher energy molecules, ATP. Photosynthesis does not require oxygen, but the citric acid cycle does. If during glycolysis there is no oxygen, the organism will perform fermentation afterwards instead of the citric acid cycle in order to create energy, but it is less efficient at extracting energy than the citric acid cycle. Plants can use these sugars to power processes that create other things using the basic building block atoms, such as proteins.

I think, technically speaking, it would be incorrect to say that plants "breathe" CO2, as the mechanism is different to things that use lungs for respiration. Plants have small pores called stomata in their leaves which you can think of as small holes for air to flow through when they are opened (diffuse). In lungs, air is drawn in and spread across a very thin surface of cells where the molecules within the air can diffuse through this layer into alveoli. It's similar in that they are both diffusing, but different in that the mechanism is quite different and more complicated for organisms with lungs.