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A SVM classifier requires a fixed-length feature vector, i.e., all feature vectors must have the same length. There are multiple solutions: Pad out the strings to fixed length. … I don't think a SVM is the right tool for that job -- this sounds like an XY problem. …

Yes, they can overfit too. Overfitting is especially a risk when the number of features is much larger than the number of samples in the training set.

A SVM with a polynomial kernel is a SVM classifier. A kernel perceptron is a perceptron classifier, or in other words, a neural net. A SVM is quite different from a neural net. … -- a SVM with a linear kernel is similar to a single-layer perceptron classifier, in case that's what you were thinking of.) …

Algorithms for finding a maximum-largin linear separator are described in the literature on SVMs (that's exactly what you need to do to train a linear SVM). … In other words, you can map the points to the new space, then can take those mapped points and train a linear SVM on them. That's conceptually how to do it. …

The first line of your equation for $d$ is incorrect. It should be $$d = \left\|\vec w\frac{\vec x_+\cdot\vec w}{\vec w\cdot\vec w} - \vec w\frac{\vec x_-\cdot\vec w}{\vec w\cdot\vec w}\right\|.$$ …

This is not answerable without knowing something about the data itself and where it comes from and what it means. But it sounds like you're trying to do something awfully dubious. It sounds like you …

SVM doesn't take into account that prior knowledge about the distribution of the classes, so if you want a classifier that takes advantage of that, you'll need a different classifier. …

Minimizing $\|\theta\|$ is equivalent to minimizing $\|\theta\|^2/2$, in the sense that the minimum is achieved for the same value of $\theta$. Since our goal is primarily to find $\theta$, this subs …

This is known as a "model extraction attack", and there's a line of research in the computer security literature on this problem. For instance, you might look at the seminal paper by Papernot et al o …

Then apply the SVM on the feature vector of length 147. SVM doesn't care where the individual numbers came from. Code is off-topic on this site. …

This is called top-3 accuracy. See https://stats.stackexchange.com/q/95391/2921, https://stackoverflow.com/q/37668902/781723, https://stats.stackexchange.com/q/156471/2921. Sure, you can use it. Wh …