That would be me :) No, the preceding letter matters. Some letters (د،ذ،ر،ز،ؤ) have no medial form-- they take the terminal form instead, and the following letter takes the initial form.
There are patterns (17 by my count?) among which letters differ only minorly, so it's not as bad as learning four forms for each letter, but there are some additional gotchas too. For example "ل-ا" ("laa") is always written as a single character "lamalif": لا. (Bonus knowledge: that's also the word for "no". You can see it at the beginning of the Shahada: ...لا إله إلا الله <- "There is no god but God..." etc.)
Yeah, I'm sorry, I was highly unclear. What you said is what I meant :) I was saying that the Arabic character set is actually simpler, but vocalized Arabic becomes harder again.
I don't know if it's completely true that English has less character variation than Arabic— as you say, in English there is a choice of upper or lower-case, with occasional changes in meaning. In Arabic, the form of a letter is completely determined by the letter it follows. It's purely a display difference, not a separate character set. There are the diacritics to think about, but outside of the Quran they are simply ignored.
That's still a big problem for a universal language of the internet though, since written Arabic is highly non-phonetic.
It's way dialectical, of course, but in MSA at least 'ز' is a [z] sound, 'ث' is a [θ] (as in "three"), while 'ذ' and 'ظ' are variants of [ð] (as in "the")— with ظ being the pharyngealized version, similar to 'د' and 'ض'. The differences are much easier to hear than to reproduce :P