How to explain a relationship between Accuracy and F1 Score / F-Measure?
Saying that accuracy is measured to get how accurate the model performs, and F1 is how well the model performs

This doesn't mean anything, it's obviously too vague.
The first things to check in order to understand this relationship are the definitions of accuracy and F1-score.
Wikipedia has a good page which explains how different classification evaluation measures are related.
Observations on your results:

The accuracy and F1-score are almost identical everywhere. This suggests that your data is probably quite well balanced, i.e. the difference in the number of positive vs. negative instances isn't very big. Why? Because if the data was imbalanced then the model would over-predict the majority class, and this would cause the F1-score to be much lower than the accuracy: assuming the majority class is the negative class, the recall would be somewhat low but the accuracy could still be high because most instances (majority class) would be correctly predicted.
As a consequence, there's no insight to gain from analyzing the relationship between accuracy and F1-score since they're virtually identical. The small differences might be due to the geometrical mean between precision and recall. F1-score is more informative in case of imbalanced data, but this is not the case here.
The F1-score is calculated only on the training data. It would be more useful to calculate it on the validation data.
There's some serious overfitting happening especially with the high learning rates, but with the low learning rates the fact that difference between training and validation accuracy increases is also worrying. Maybe the model is too complex or there are not enough instances in the data. Ideally the two accuracy values should converge.