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Disclaimer: i am one of the authors of the referenced link.
If you are doing pure image classification/segmentation, I would say no.
I would not store the output of convolution layers, noramlly. In principle, the output of models can be stored in the feature store, however.
Feature stores store data in tabular file formats (like parquet) and are used to ...
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For your first question, yes, it is optimized for that size since the original paper for Xception used 299x299 size. But, you can use other sizes. You should resize your images to 299x299 that would be the best.
For your second question, the reason height = width because in the network, the convolutional filters which are used are square (3x3 filters). The ...
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A rule of thumb, as you go deeper, number of filters increase and the size of filter remains same or increases. You don't follow both of them. This will help your network learn.
Then, consider increasing the number of filters in proper fashion if still your network is not learning.
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1 - Activation functions are non-linear functions. These are added in between layers which are simply Linear transformations.
Example without activation function:
ConvLayer1(Input) -> ConvMaps1
ConvLayer2(ConvMaps2) -> ConvMaps2
Mathematically, this would be $I_{nput} \circledast K_{ernel_1} \circledast K_{ernel_2} $,
which is equivalent to $I_{nput} ...
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A common approach is what you suggest in 1. - apply time-shift as a Data Augmentation strategy. The augmentation is generally beneficial with deep learning models, and GPUs are fast so the compute time is rarely a big problem.
Another strategy, less common, would be to make sure that the event is always located at the same position inside the analysis window ...
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