Make sure you understand the algorithms before using them.
E.g. k-means minimizes variance, and of course an attribute with a larger scale, with have a much larger variance, too. Therefore, standardizing data is often beneficial there.
But with e.g. hierarchical clustering, you need to give a distance function. Euclidean distance is just one of the many options; and maybe you can be much more specific as to which attribute should have which amount of effect on the result.
The key question is: what is a sensible measure of similarity for your domain. There is no universal measure. With hierarchical clustering, this is just more explicit - K-means is based on the sum-of-squared-deviations, so there you need to rescale / transform your data to give appropriate weight, which is much more limited than specifying a similarity measure for your data.
So: when are two soil samples alike - as you can see this is a domain and purpose question, not so much a statistical question.
You should probably standardize your data before PCA.
PCA involves projecting the data onto the eigenvectors of the covariance matrix. If you don't standardize your data first, these eigenvectors will be all different lengths. Then the eigenspace of the covariance matrix will be "stretched", leading to similarly "stretched" projections. See here for an example of this effect. This is not what you want. See also here for several good answers describing the geometry of PCA.
However, there are situations in which you do want to preserve the original variances. See here for discussion on that topic.
As for your follow-up question, of whether you will lose dependencies between variables if you apply standardized independently: the answer is no. In fact, correlation between un-standardized random variables is equivalent to the covariance of standardized random variables.
Do note that covariance is inherently a measure of linear association. The covariance between a uniform random variable on $[-1, 1]$ and its square, for example, should be exactly 0. So higher-order relationships between variables could in fact be discarded by PCA. This is one motivation for kernel PCA.
Best Answer
The Wikipedia page on "Normalization" notes:
It then goes on to list 6 examples of "normalizations in statistics," including both of what you have called "standardization" and "normalization."
"Normalization" onto [0,1] is called "feature scaling" or "unity-based normalization" on the Wikipedia page. "Normalization" based on the observed mean and standard deviation (called "Student's t-statistic" on that page; "standardization" in more frequent but not universal usage) is typically what you want for PCA.
This type of terminological confusion happens often in practice. Consider, for example, the frequent use of "multivariate" to represent multiple predictors in a model, when that word might best be reserved for situations with multiple types of outcomes.
So I wouldn't worry too much about the terminology that other people are using. Look into what they actually did, not what they called it. Then when you report your study, explain clearly what you did and try to use the best current terminology yourself.