I've managed to learn Hiragana now, and I've started to begin to be able to "read" it. At the moment, I still have to interpret each symbol and then piece the word together (or with longer sentences, right the romanji down after deciphering the hiragana). How long does it take, approximately, to be able to read it just off the bat?
That depends. The speed at which you can read hiragana will increase at the fastest rate, because you obviously see it more often than katakana. Again it's all about how much you practise.
Also, how do you know where the words end with some sentences? Sometimes there is a full stop or gap, other times there isn't.
Yeah, Japanese doesn't really use spaces and you tend to have to use the changes in the ways words are written (hiragana, katakana, kanji) to figure out the differences between the words. Again, you just become accustomed to it. For example there are no breaks in the following sentence (I was told off by Takahashi sensei), but it should be pretty obvious where the breaks in the word are:
俺は高橋先生に叱られました。
The first kanji is おれ (a way of saying 'I' used exclusively by males), the next hiragana is your particle は, the next two kanji are a name たかはし, and the two immediately following that mean せんせい (teacher.) The next hiragana is another particle に, and the final kanji signals the start of the verb 'to scold' しかる, in this case conjugated into the past/passive form. There's really no hard and fast rule, and you can get a long run of kana/kanji without any change to indicate a change in the word (東京国際会社), so again it is just a case of getting used to reading the language.
And once I learn Katakana, where next? Do you go straight onto some simple, common kanji, so you know the popular nouns, verbs and adjectives, or do you get the grammar stuff sorted, using kana, then move onto learning what to put in sentences?
Yeah, best thing to do is to get yourself a textbook which uses kanji (it will put the reading in furigana above the word), and start to expose yourself to kanji in that way. That will also help you read the language as it is usually written, which comes back to your second point, above.
I was also thinking of getting Heisig's "Remembering the Kanji Vol.1 ". I know that this is only a memory technique and that actually reading the meanings behind the kanji follows in his second and third volumes, but people seem to be saying that it is a very reliable method for remembering the 2000 kanji promoted by the Japanese government.
I have quite a good memory, so I think this book may be a useful way to commit kanji to my bbbbbrrraaain. Problem is, he uses an unorthdox order, so I'd have to stick with it. I'd also have to read the other two volumes in all likelihood.
I have no experience of the other textbooks which you posted, but I do have a copy of Heisig's book. You might be different, but I have never really used it. Far too waffly and pretentious. I have just had a look through to try and give you an example of the ways in which he tries to teach you the kanji, but it really is a load of rubbish. You can probably find extracts online if you want to have a look. He tries to give each kanji a story to help you remember the stroke order. Needless to say, I only have the first volume.