How much mulch fits in the back of my pickup truck?
We don't know. All trucks are different. Average is 1.5 cubic yards.
How much dirt can I get in the back of my pickup truck?
Average is 0.5 cubic yards. The problem here is not how much you can fit, but how much the dirt weighs.
Should I bring a tarp?
It would be smart. Especially for mulch or dirt. It is up to you. After you leave the property, your load is your responsibility.
Can I get less than 1 cubic yard loaded?
Yes. It's just priced by the cubic yard. So, people get ½, ¼, ¾ yards loaded all the time. Depends what you can carry.