Doesn't the etymology of quando already explain that? I don't know where quam comes from, though. But cum and quam seem like the masculine and feminine accusative case forms of a pronoun, and are parallel to tum and tam. Their PIE forms would then be Template:termx, Template:termx, and Template:termx, Template:termx. Why the accusative is significant here I don't know, but it is certainly striking that these words have exact parallels in Gothic.
Aha, yes, and that leads right to modern EN then / than, and modern DE wenn / wann, no? Interesting how the feminine a forms remain comparative / interrogative.
Do any of you know if there's a reason for the questions beginning in qu- being answered by the same thing begiining in t-? (Actually, they're often non-answers; imagine the conversation "Qualis?" - "Talis.")
More or less, yes. Those forms have actually been extended with a further suffix, of which the origin isn't known. The masculine accusative pronouns have an extra unidentified suffix. Gothic and Old Norse are the only Germanic languages that seem to have retained the unsuffixed forms, but only in their adverbial meaning. Compare 𐌸𐌰𐌽 (þan, “then”) and 𐍈𐌰𐌽 (ƕan, “when”) with the accusative pronoun forms 𐌸𐌰𐌽𐌰 (þana) and 𐍈𐌰𐌽𐌰 (ƕana). The Germanic languages also have no trace of any adverbs based on the feminine forms, like Latin has.
The difference between the -e- forms and -a- forms is not Germanic, but developed independently in Middle English and Middle or Modern German. It doesn't occur in any of the other languages, which use the same word for both.
There is no specific reason for the qu- and t- being parallel, it's just a matter of meaning. *kʷ- was the stem in PIE that was used to form interrogatives, while *t- was the stem used to form demonstratives. There were other stems in use for demonstratives too, but *t- was by far the most common and general in use.