Here is explanation for the terms:
Exogenous - determined outside the system/model being studied. For example, if you study macroeconomic model without explicitly modelling weather patterns, bad weather can be interpreted as an exogenous shock that affects output of agricultural sector.
What exogeneity means will be explained in virtually any undergraduate textbook that uses some models, even outside economics.
Stationary Distribution - distribution of stationary process. Stationary process is a process that satisfies some conditions such as that mean and variance do not change in time. Distribution of white noise random variable is one example of a stationary distribution.
You can have look at a chapter 7 from A Primer in Econometric Theory by Stachurski for more details and rigorous explanation.
Finite Bounded Support - support of a probability distribution can be thought of as the set of values the distribution is able to take with positive probability (i.e. values over which there is some density including values at the boundary). For example, support of normal distribution is from $(-\infty, \infty)$, support of Poisson distribution is non-negative integers etc.
Finite means the support does not include infinity (like normal distribution) and bounded means that the distribution lies between some two concrete values. For example distribution with support $[0,1]$ is a finite bounded distribution.
You can read more about this sort of stuff in any statistics/econometrics textbook. The primer in econometric theory I mentioned above is good graduate level starting point. If it is too advanced you can pick up any undergraduate statistics textbook.
