Plants produce carbon dioxide all the time because of respiration, but during the day (when there is light), they use CO₂ for photosynthesis, and fix CO₂ into other molecules, giving as end product O₂ more than CO₂. This is why it is called carbon fixation. On the other hand, when it is dark, plants do not have an energy source for photosynthesis, and so cannot fix CO₂ and produce O₂. The process is light-independent, and more formally known as the Calvin cycle. During this cycle, 3 carbon dioxide molecules are absorbed to produce the small sugar G3P (glyceraldehyde-3-phosphate) for the plant to use elsewhere. Two G3P molecules are required to make glucose.

As for comparing the amount of carbon dioxide and oxygen between night and day it depends on how you look at the sample region. You can consider anything from the block you live on to the entire Earth. If you only consider your block during the day, large amounts of carbon dioxide are produced from higher activity levels with humans, animals, and driving of vehicles. Additionally at this time, any living plants are producing high amounts of oxygen. At night, plants take in carbon dioxide reducing it's levels; however, humans and animals are still producing it.

When considering these fluctuations between oxygen and carbon dioxide you also have to consider the overall atmosphere composition before you start the "experiment". We start with ~21% Oxygen, and ~0.04% carbon dioxide. Even though there is an increase in carbon dioxide through the daytime on your block, oxygen is much more present at the beginning of the day.

This question really highlights the reason climate change is occurring due to increases in greenhouse gases (carbon dioxide is just one of many). Although plants do a great job of eliminating carbon dioxide, they can't keep up with the additions that we use during the day. If you are interested in looking at the changes in oxygen and carbon dioxide an isolated area, I'll suggest that you look into the Biosphere 2 owned by the University of Arizona. They have completed some really cool research.

Lastly, addressing the idea of taking in oxygen in the morning - since our atmosphere is comprised mostly of nitrogen (~78%) followed by oxygen (~21%) and some other gases (including carbon dioxide), we take in many gases in the morning! If there were no oxygen, then it would be a major health hazard, as we require oxygen to continue life. So overall, even though the concentration of carbon dioxide is increasing, it's levels are many times lower than oxygen.

Great question! You are correct that plants produce both CO₂ and oxygen. A lot of people don’t even understand that plants do both cellular respiration ( sugar + oxygen → carbon dioxide + water) and photosynthesis (carbon dioxide + water → sugar + oxygen)

Here’s the thing, plants are doing cellular respiration all day, too! Cells use a form of energy called ATP that they get by doing cellular respiration. They can’t use the energy in the sugar they make until they break it down into ATP.

All of the cells in a plant do cellular respiration, but not all do photosynthesis. Look at a tree. How much of it is green? The entire tree (except the outer bark) is living cells. Some are deep inside the trunk or roots. They never do photosynthesis. So where do they get their energy? From the sugar that the leaves make. The sugar and other stuff move around in the tree sap. The cells that don’t do photosynthesis are doing cellular respiration all day long to get their energy from the sugar.

Air moves and mixes a lot too, so you won’t actually find a difference in the CO₂ concentration of the air between night and day.

But you can find a difference in CO₂ concentrations in lakes that have a lot of algae. Algae are not really plants, but they do photosynthesis and cellular respiration. Almost all of their cells can do photosynthesis, so they can make a lot of oxygen during the daylight hours. At night, they are using up the oxygen like crazy and making a lot more CO₂. The CO₂ combines with water to make carbonic acid. Acids lower the pH of the water. In lakes with a lot of algae, the pH can change drastically between night and day.

Which do you think takes in more CO₂ per cell, a tree that has just sprouted, or one that is mature?

You might want to think about a career in plant ecology if these sorts of questions interest you.

Plants make a lot more oxygen than they produce CO₂ (remember: most of the plant's body is made out of carbon-containing compounds. That carbon didn't get released as CO₂ during the night, but the oxygen associated with it did get released). I don't know when the minimum oxygen concentration is, but I guess it would be in the early morning shortly after dawn, as you say. Incidentally, temperature does the same thing, for related reasons (no energy coming in during the night...).