SVC has C and gamma parameters ( https://scikit-learn.org/stable/auto_examples/svm/plot_rbf_parameters.html )
Are there any similar parameters for an SVR (support vector regressor) as well ?
Yes. For example, see, please, Matlab function fitrsvm with parameters
'BoxConstraint' (i.e. C) and 'KernelScale' (i.e. gamma).
Yes, svm needs these two parameters. see sklearn.svm.SVR
It depends on SVR type you use
for example in kernel RBF ===> C, gamma, epsilon are hyper parameters.
but for kernel poly and sigmoid ======> C, gamma , epsilon, degree, coeff are hyper parameters.
For more information see the following example.
https://scikit-learn.org/stable/auto_examples/svm/plot_svm_regression.html#sphx-glr-auto-examples-svm-plot-svm-regression-py
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