If I have a experimental study with a treatment and control groups. My independent variables are the administered drug/placebo and the dependent the blood potassium levels, which were measured before and after the treatment/placebo for each subject. Should I use a paired t test or an independent samples t test to analyse the data? Cheers

In this setting, given successful randomization and balance in baseline values, you should only have to model the post-values. Given the distribution in expected values is fine, an independent ttest should be fine (average treatment effect) or you may need to move over to something like quantile regression (comparisons in medians) if the small samples results in some skewness and the central limit theory tendency isn't quite reached.

I would nevertheless include the baseline into the analysis, because it increases statistical power
to have a within-person control. You could simply calculate the intra-individual pre-post differences
and compare them between groups, using independent samples t-test or U-test.

balls my old fruit. data is non-parametric precisely when it is not parametric.

Let T be the set of tests known to dason, then T = {t-test, U-test}. Let P_T(t|X) be the probabilty that dason chooses test t for data X. Data X is non-parametric when P_T(U-test|X) >0.5.