Does a cell take in oxygen and nutrients from the environment? How did the first cell form?

A cell takes in nutrients, and it also respires, i.e. exchanges oxygen, to combust the sugars that it takes in (of course the cell could be photosynthetic, but it would nevertheless have to take in $C {O}_{2}$ to convert to simple sugars).
As to how a cell originally formed, you got me. $\text{Abiogenesis}$ is a perennial topic in the creation/evolution debate. Most biologists would be intellectually honest enuff to confess that they don't know how the first cell formed; there should be an equally honest admission by creationists that they don't know either - at least they cannot advance convincing evidence for their proposal.