When atmospheric carbon dioxide samples are being collected, can natural occurrences (e.g., volcano and lava gases in the atmosphere) affect the collection? How is it possible to collect samples from just human-caused emissions, while there is CO2 in the atmosphere from natural occurrences?

Very good point! Single measurements of CO2 concentrations cannot tell you where the CO2 came from. (It could be natural or anthropogenic [manmade].) Back in 1957, Charles Keeling and his contemporaries interested in the composition of the atmosphere chose to take air samples in "clean" sites so that they could eliminate the rapid variations in concentration that might occur near a [carbon] source or sink. (The measurements inside a city are strongly influenced by traffic patterns, for example.) They hoped to simply determine what the background concentrations of CO2 were like. This record of measurements shows a long-term increase and accumulation of CO2 in the atmosphere due to fossil fuel consumption but not much more about specific details of how much, where and when CO2 is put into or removed from the atmosphere.

The premise that man causes global warming tells me that man can control natural CO2 emissions that have been occurring since the beginning of the Earth.

Man cannot control natural emissions. Without people, the concentration of CO2 in the atmosphere would be balancing between the amount released by respiration (i.e., animals and plants) or from warm ocean water, and the amount absorbed by plants (i.e., for photosynthesis and growth) or in colder ocean water. We disturb this balance when we burn fossil fuels and have steadily added to the atmospheric concentration. This increase has led to global warming from the equilibrium climate of pre-industrial times.

Can one blast from a volcano affect readings over most of the globe for an extended time?

Overall, volcanoes release about 5 percent of the equivalent amount of CO2 released by humans. Quite small. However, about once every 20 years there is a volcanic eruption (e.g., Mt. Pinatubo, El Chichon) which throws out a tremendous amount of particles and other gases. These will effectively shield us enough from the sun to lead to a period of global cooling. They typically dissipate after about two years, but the effect is nearly global.