Am I wrong in thinking that a phonetical language, for example Spanish, is a language where the words are spelt as they sound
I don't think that a language itself is phonetic in that sense. It is the written form that can be described as phonetic or not.
Apart from that I would say you are correct. Note that written Spanish is not 100% phonetic. For example 'g' is pronounced differently according to which vowel it precedes and some varieties make no distinction in sound between 's' and 'z''.
There is no such thing as a phonetic alphabet. It's a myth popularized by people who either can't see the forest for the trees or have little knowledge of the language they have in mind, at least where European languages are concerned. European alphabets are ancient-Greek-based. No language today even remotely resembles ancient Greek pronunciation. Apart from that, the number of sounds a language has exceeds the number of letters in any Greek-based alphabet by orders of magnitude.
Attempts have been made to create phonetic alphabets, most of them in the beginning of the 20th Century. None of them were successful. What G.B. Shaw pointed out (in the preface to his play "Pygmalion") is still true today: the most frequently used vowel in the English language does not have its own letter.