How to use a sample from the posterior predictive distribution Suppose I have a sample drawn from a posterior predictive distribution of a previously trained Bayesian Network (or any other Bayesian model). I.e., I have a vector $\tilde{\textbf{y}}_n = [\tilde{{y}}_1, \tilde{{y}}_2, ..., \tilde{{y}}_n]$, where all elements are data points drawn from $\text{P}(\tilde{y} | \textbf{y})$.
My question is: What are the ways in which Bayesian statisticians would commonly make use of this sample, drawn from the predictive posterior distribution? Are my following three suggestions correct? Are there other ways?

1. Point estimate
We can summarize the sample vector $\tilde{\textbf{y}}_n$ with $1$ single scalar, that would represent our "prediction". For example, we could take the sample mean.
$$E[\tilde{y} | \textbf{y}] = \frac{1}{n} \sum_{i = 1}^{n} \tilde{y}_i$$
2. Probability estimate
We can compute the probability of having a future value larger than (or smaller than) a certain value. For instance, we might want to compute the probability that the future value will be larger than 8.5. Then, we could simply take the proportion of the elements in our sample vector $\tilde{\textbf{y}}_n$ that are larger than 8.5.
$$\text{P}(\tilde{y} > 8.5 | \textbf{y}) = \frac{1}{n} \sum_{i=1}^{n}{\textbf{1}_{\tilde{y}_i > 8.5}}$$
3. Prediction interval
Suppose that we want a prediction interval, in which 95% of the future values will lie. Then, we would simply take the 2.5th percentile from $\tilde{\textbf{y}}_n$ as lower bound and the 97.5th percentile from $\tilde{\textbf{y}}_n$ as upper bound to get the prediction interval:
$$\text{95% prediction interval: } (2.5^{\text{th}} \ \text{percentile}, 97.5^{\text{th}} \ \text{percentile})$$

There's an unlimited number of uses. You can calculate the statistics you've shown, but also any other statistics (median, mode, standard deviation, etc), or any arbitrary functions, you can plot the posterior predictive distribution instead of calculating the intervals, you can do hypothesis tests, you can use it for decision making, e.g. find the conditions such that function $h(\tilde y)$ is maximized, etc. Same as you can use statistics to learn something about your observed data, you can use them on the predictions to make claims about the possible outcomes as predicted by the model.
