How to start prediction from dataset?
The problem you are facing is a time series problem.
Your events are categorial which is a specific case (so most common techniques like arima and Fourier transform are irrelevant).

Before getting into the analysis, try to find out whether the events among nodes are independent. If they are independent, you can break them into sequences per node and analyze them. If they are not (e.g., "Main power supply has a fault alarm" on node x indicates the same event on node y) you should the combined sequence. Sometime even when the the sequence are dependent you can gain from using the per node sequence as extra data.

You data set is quite large, which means that computation will take time. You data is probably noisy, so you will probably have some mistakes. Therefore, I recommend advancing in small steps from simple models to more complex ones.

Start with descriptive statistics, just to explore the data. How many events do you have? How common are they? What is the probability of the events that you try to predict? Can you remove some of the events as meaningless (e.g., by using domain knowledge)?

In case you have domain knowledge that indicates that recent events are the important ones, I would have try predicting based on the n last events. Start with 1 and grow slowly since the number of combinations will grow very fast and the number of samples you will have for each combination will become small and might introduce errors.

Incase that the important event are not recent, try to condition on these events in the past.

In most cases such simple model will help you get a bit above the baseline but not too much. Then you will need more complex models. I recommend using association rules that fit your case and have plenty of implementations.

You can further advance more but try these technique first.

The techniques mentioned before will give you a model the will predict the probability that a node will be down, answering your question (ii). Running it on the sequence of the nodes will enable you to predict the number of nodes that will fail answering question (i).