There are two types of readings, so the question isn't as simple as it would be in Chinese languages. When kun readings are involved, it gets a bit complicated. When you're talking about on readings, yes, 1 kanji = 1 morpheme, but keep in mind that there are bound and free morphemes, so it's not always the case that 1 kanji = 1 word. Put another way, 1 morpheme does not necessarily equal 1 word. You're going to need to learn words to know where the boundaries are. This can be challenging when authors don't use enough kanji, but generally speaking kanji show word boundaries fairly well, so spacing isn't really needed (although there are times when it could be helpful). Let's look at some examples.
話す -- hanasu; this is the word for "speak".
会話 -- kaiwa; this is the word for "conversation".
電話 -- denwa; this is the word for "telephone".
話題 -- wadai; this is the word for "topic".
Here you can see in the first instance we have a word written with a kanji and a hiragana (known as okurigana when it shows inflectional endings). You can say that 話 represents hana-, which is the verb stem, I suppose, but since we aren't talking about conjugation, I don't feel like that's appropriate. That could just be me, though. Anyway, it's only pronounced this way when there is す or one of its inflections afterwards. In the other cases, as you can see, it's pronounced wa. In the case of the on reading (wa), it's a bound morpheme -- it can't stand on its own as a word.
Now, this one is a bit tricky, because there is the word 話 (hanashi), which comes from the verb 話す and means "story". This is a case of not using okurigana because everybody already knows the word already and how to read it, and it also stands in contrast to 話し, with the same pronunciation, and is the continuative form of the verb 話す.
Does that pretty much answer your question?