Given conjugate prior and posterior distributions, what is the PRIOR predictive distribution?

Question

I am doing an assignment on my statistics class. We had 1 lecture about bayesian parameter estimation, where we were taught about the following formula (and it's discrete form, if $h(\theta)$ was discrete). It was said that $f(\theta|x)$ is the posterior, and $h(\theta)$ is the prior.

$$f(\theta|x) = \frac{f(x|\theta)\cdot h(\theta)}{\int f(x|\theta)\cdot h(\theta) d\theta}$$

We were then taught that in order to estimate the actual value of $\theta$, we were to use $$E(f(\theta|x)) = \int \theta \cdot f(\theta|x) d\theta$$

I managed to understand these formulas and how they work. We were then, however given the following problems which I was unable to solve:

Assume there is a random variable $X \sim Po(\lambda) $ that specifies the number of server connections over a single millisecond. There is an expert estimation that there should be $2$ connections every millisecond. Furthermore, there is a set of $100$ samples that were taken over the course of $100$ms (they were included in a .csv file). Knowing this:

1. Show the graphs of prior and posterior distributions of the parameter $\lambda$
2. Show the graphs of prior and posterior distributions of the variable $x$
3. Show a $95\%$ confidence interval in the prior and posterior graphs of the distribution of $\lambda$ and compare them
4. Choose $2$ posterior point estimates of $\lambda$, compare them, and justify your selection
5. Choose $1$ prior and $1$ posterior point estimate of the variable $x$ and compare them

Furthermore, the only resource we were given was the following wikipedia page. From what I gathered, we are probably supposed to construct the prior function $h(\lambda)$ from the table for Poisson distribution:

However, our materials made no mentions of conjugate priors, so I am only guessing here. I managed to determine that my conjugate prior distribution is the Gamma function with $\alpha=2$ and $\beta=1$. This allowed me to generate the graph of the prior distribution of the parameter $\lambda$. However, the table made no mention of the type of distribution for the posterior of the parameter, so I can only assume it is also Gamma. Furthermore, the table makes no mention of the prior distribution of $x$, and also does not explain what do $\alpha'$ and $\beta'$ mean in the context of the posterior predictive. Please, I'm asking for someone to help me understand what I am supposed to do.