Question

1. How can a marginal product for a resource change?
2. What can change the demand for a resource?

Thank you for your help and in explaining how this is so.

Answer 1

1. The marginal product of a resource may change in several ways. The chief positive change that you might see in this will probably be caused by advances in technology - say, better drills in mining, or more fuel-efficient engines for the transportation of ore from mine to refinery. Other positive boosts to marginal product may come from finding richer deposits of a resource, or from finding ones that are easier to exploit - though, nowadays this does not happen quite as often as it once used to. Other positive effects may come from a drop in general wage level, taxation, etc. - essentially anything that lowers the cost of extracting one unit of a resource.
Conversely - negative effects on the marginal product come from things that make extraction of the resource more costly. Wage increases, tax increases, depleting resource pools, natural disasters - all of these things might make marginal product lower.

2. The demand of a resource is determined by.. well, the demand of the resource. What goods can be created with the resource? How much of that good is demanded? Can the good be substituted by another that does not require the resource? Can the resource be substituted in producing the aforementioned good?
The demand of the resource, and the goods that require the resource to be made are both also affected by the general state of the economy. Higher taxation might reduce available disposable income in the economy, which would reduce demand (unless it is an inferior good, in which case lower income will raise demand). Lower interests rates could increase available income and thus increase demand (similar caveat on inferior goods).

I am probably making it sound a lot more complicated than it is by introducing inferior goods into the mix, but for normal goods it is rather straightforward - and common sense will generally answer your question for you.