I almost write everything as it is and without paraphrasing or even citing, is that plagiarism?
Yup -- submitting work created by somebody else (the author of the textbook or course book) without crediting them is absolutely plagiarism. The solution, as you point out, is to cite them.
More worryingly for your educator, reading someone else's content -- even if properly cited -- makes it hard to evaluate whether you've understood the material. If the question is "How does pigeon domestication support the theory of natural selection?", you could quote directly from Charles Darwin's Origin of Species, chapter 1 --- but all that does is show that Darwin understood the connection! It's not clear if you understand the connection and, if I was grading your work, I'd want to know if there's evidence that you understand natural selection well enough to find a connection.
Other times, I get some ideas from outside the book and I do cite them in that case, however I do not paraphrase as I am learning by heart the thoughts in order to answer a specific question in the exam, is that plagiarism? (e.g. lack of paraphrasing)
Direct quotation isn't plagiarism as long as its properly cited; however, as I pointed out earlier, saying "Darwin (1859) believes that the connection between domestic pigeons and natural selection is ..." doesn't tell your evaluator much about whether you understand the connection, which is what they're trying to evaluate.
And lastly, since I am memorizing by heart, I sometimes misspell the name of an author or even change a bit of details in his or her idea, is that a bad thing?
For a closed book exam, definitely not -- it's understandable that you can't cite a work that isn't in front of you. For an open book exam, it would depend on your subject area: I teach biology, and I routinely overlook grammatical, spelling and minor mathematical errors as long as it's clear the student understands the biology they're describing.