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Which data mining or machine learning algorithm would be appropriate for learning ordered frequent patterns?

Sequence mining seems the thing you are looking for. Used quite extensively in problems with ordered data, e.g. mapping DNA sequence -> disease. There are algorithms like SPADE and PrefixSpan.
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How do I calculate the accuracy rate of predicting “Fail”? Am I supposed to create a confusion matrix?

Strictly speaking, calculating accuracy doesn't require the details of a confusion matrix: it's simply the proportion of correct predictions. Since there are 4 possible classes in this exercise and we ...
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What to do if the model is not performing well on a validation dataset

Just a few comments: You probably don't need SMOTE if your data is only slightly imbalanced. It can be a source of bias. 30% accuracy is extremely low: there's probably a mistake somewhere, your ...
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Data preprocessing methods

Here are some. Dealing with the variable Types. Dealing with Missing data Encoding categorical variables Categorical variable — cardinality Categorical variable — rare labels Dealing with Outliers ...
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What is the formal category of problem described by identifying consecutive occurrences of attributes in records?

What you describe is feature engineering, or specifically handcrafting feature. Specifically, sequence detection is the indeed the term for crafting features like "team X lost their last 5 games&...
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how to deal with columns that has different value in only 1 or 2 rows?

In other words, you have sparse binary features. A vast majority of the data is zeros. The remaining data are ones. One option is to transform the features to be denser. This can be done with ...
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