Expanding on my comment, The main goal of your training algorithm is to decrease the net loss. So as long as your validation loss is decreasing, your algorithm is doing good, and is generalizing well. But the validation accuracy is not improving or getting worse, consider relooking at the loss function you are optimizing, it indicates that the loss function is not suitable for the task, rather than training algorithm/model being defective. Go for some other loss function, and then select a model/algorithm that is suitable for that loss function.
Yes, absolutely. First of all, overfitting is best judged by looking at loss, rather than accuracy, for a series of reasons including the fact that accuracy is not a good way to estimate the performance of classification models. See here:
https://stats.stackexchange.com/a/312787/58675
Why is accuracy not the best measure for assessing classification models?
Classification probability threshold
Secondly, even if you use accuracy, rather than loss, to judge overfitting (and you shouldn't), you can't just look at the (smoothed) derivative of accuracy on the test curve, i.e., if it's increasing on average or not. You should first of all look at the gap between training accuracy and test accuracy. And in your case this gap is very large: you'd better use a scale which starts either at 0, or at the accuracy of the random classifier (i.e., the classifiers which assigns each instance to the majority class), but even with your scale, we're talking a training accuracy of nearly 100%, vs. a test accuracy which doesn't even get to 65%.
TL;DR: you don't want to hear it, but your model is as overfit as they get.
PS: you're focusing on the wrong problem. The issue here is not whether to do early stopping at the 1th epoch for a test accuracy of 55%, or whether to stop at epoch 7 for an accuracy of 65%. The real issue here is that your training accuracy (but again, I would focus on the test loss) is way too high with respect to your test accuracy. 55%, 65% or even 75% are all crap with respect to 99%. This is a textbook case of overfitting. You need to do something about it, not focus on the "less worse" epoch for early stopping.
Best Answer
This can happen because classification accuracy is a discretized result. Consider a binary classification (e.g. human vs animal), i.e. output layer having one neuron, and you use a threshold, let's say 0.5. At some level, your model might produce results very distinctively for your validation set, which is a good point in your learning process, i.e. for human it gives values around 0-0.1, and for animal, it gives values around 0.9-1. Suppose it starts overfitting afterwards, these predictions might get close to 0.5 from each side, increasing your validation loss, while your validation accuracy stays the same. It might also increase some time, while your certain cases' certainty decreases. The case of being larger than the initial cross-entropy for the validation set is not impossible in this case, though a very special one.