Will this actually make espresso?
No, and the phrase espresso style on the box means concentrated rather than genuine espresso. Real espresso depends on a pump forcing water through finely ground coffee at high pressure in under a minute. The pressure here comes from your arm pushing a plunger down a sealed chamber, nowhere near that. What you can make is a short, concentrated brew using less water and a finer grind, which behaves like espresso in a recipe: dilute it with hot water for something close to an americano, or add steamed milk for something close to a latte. What you will not get is crema, the fine foam only genuine espresso pressure produces, or quite the same body.
How do I adjust the variables to change the taste?
Each has a predictable effect, and they are worth changing one at a time. Grind size controls how fast water passes through the coffee: finer for a stronger, slower brew, coarser if it tastes over extracted or the plunger is hard to push. Water temperature changes what dissolves, since cooler water pulls out less of the bitter compounds and suits darker roasts, while lighter roasts generally want it hotter. Brew time before pressing changes strength directly, and the ratio of coffee to water sets the concentration. Start with AeroPress's own instructions, then adjust grind first, since it has the largest effect on the result.
What is the inverted method, and should I use it?
It is the well known alternative to the standard method: the brewer is assembled upside down, with the plunger inserted first, so the coffee steeps in a sealed chamber and nothing drips through until you flip it onto the filter cap and press. It gives you full control over steep time without the coffee draining early, and it is worth trying once you are comfortable with the standard method.
Is the paper filter better than a metal one?
For a cleaner, less bitter cup, yes, and that is the main reason. Paper holds back the coffee's oils and the fine particles that a metal mesh lets through, and those fines keep extracting in your cup while you drink, with sediment at the bottom concentrating the harshest flavors. A reusable metal filter is available if you prefer a fuller, oilier cup and do not mind more sediment.
Can I make coffee for more than one person?
Not directly. It is a single-cup device by design, with a 10 ounce capacity. You can brew consecutive cups and combine them, or brew a concentrated shot and dilute several servings from it, but there is no way to press a large batch in one cycle. If you regularly need coffee for four people at once, this is the wrong tool for that job even though it is an excellent one for a single cup.
What if a part wears out or breaks?
AeroPress backs its products with a one year warranty against defects in materials and workmanship, so a defective unit within that window is covered directly by the manufacturer. Filters are cheap but sized specifically for this device, so keep a supply of the correct ones rather than substituting a different brand's paper.