As I understand, the haka is supposed to be a traditional Maori/(other Polynesian cultures?) war dance that was performed before battles. I know it's been adopted by the New Zealand All Blacks rugby team. I saw some other national teams doing it this past summer (Canada hosted some rugby championship this year so it was on TV). In the context of sport and battle, I can totally understand that it's a means to intimidate your opponent/enemy.
However, there is a video going around of a school in New Zealand who performed (is performed the right word?) as a send-off for their teacher who had passed away. I've also seen a video in which members of the New Zealand Defence Forces do it for 3 of their fallen soldiers. What sticks with me is that there's this big build up of emotion and intimidation then nothing but silence while the hearses are allowed to go on their way.
I guess my questions are, when and how did the Haka start becoming used as a way of conveying respect as opposed to intimidation? Are there different aspects to it when it's being used in a non-battle situation i.e. does the chant change, are the movements different? Is there a specific symbolism behind it when it's performed for a funeral?
There are many types of haka, and they've always been used in just as many types of ways. Not at all solely used before battle. Think of them more as an outward expression of high emotion, rather than merely a means to intimidate. The types of haka you were initially probably imagining are called 'Peruperu', these haka were originally performed by male warriors, before a bit of the old biffo went down.
These days haka can be performed formally at welcoming's, farewells, celebrations - anything really. You really begin to understand when they are performed absolutely spontaneously as an outward show of inner respect, or joy.
It's a Haka, not The Haka. I guess most people think of the Haka performed by the All Blacks as "The" Haka, but even that has changed, from Ka Mate to Kapa O Pango, due to increased sensitivity around Ka Mate. The Ka Mate Haka was composed by Te Rauparaha, a Ngāti Toa chief, and there has always been some tension around it's use by the All Blacks due to historical animosity between Ngāti Toa and other Iwi, and issues of appropriation for Maori in general and specifically Ngāti Toa due to unsanctioned use of their Haka (see here for some discussion of this).
Traditionally Haka referred to a wide variety of recited dance with accompanying actions, my understanding is they have always conveyed some degree of respect, that the situation or person that they are being performed for is worthy of a Haka. Nowadays people tend to think of Haka being a conflict thing, but this isn't accurate, I guess it's the curse of history that the ones performed around conflict were more likely to be recorded e.g. Monkhouse's description of Maori performing Haka as they approached the Endeavour or Louis Auguste de Sainson's painting of the Haka aboard the Astrolabe. This might be worth a read if you're interested in getting into the nitty gritty behind how Haka and Waiata are situated in Maori culture.