Homer's deeper voice

The change in Homer's voice is tied to how Homer's role in The Simpsons changed.

Initially, Homer was not the main character to the extent that he ended up becoming in later seasons. That's not to say that there weren't Homer-centric episodes, but Homer was a more reasonable character back then. Still an oaf, but more of a Joe Average and not really the source of the wackiness.
Think of Homer like Al Bundy: there's nothing special about him, he's just a normal guy who usually draws the short stick. The world is crazy, and Homer/Al is subjected to this crazy world. They're still flawed themselves, but it's not their main role in a scene.

It makes sense for an unmotivated oaf to have a matching voice: low volume, low timbre.

But as Homer gained popularity, his character (and his flaws) became more outrageous and outspoken. Homer became a wacky character, with loud reactions and (stupid) convictions. These require Homer to become more outspoken, and showcase an idiot's conviction, which means he needs to speak firmer and louder. He also become more prone to vocal outbursts; not so much the "d'oh" (which he already had) but the screams or yells whenever he's excited or startled.
The Al Bundy analogy no longer applies here. Homer has become the source of crazy, which requires him to behave differently (not just like an unmotivated oaf).

All of these changes in Homer's role required him to have a larger vocal range to match his more extreme behavior. On top of that, he also speaks louder, which is done to convey the (idiot's) conviction that he often touts for comedic effect. Speaking louder tends to raise the timbre of any person's voice.

This could've been an intentional change (i.e. instructed to this voice actor by the show runner), or it could've been an inevitable consequence of the voice actor needing to convey things in Homer's voice that were simply impossible (or incongruent, or underspoken) when done with the original low timbre Homer voice.

It's not explained in the show.

For question 1) In the earlier "The Tracy Ullman Show" shorts (which is where "The Simpsons") came from, Dan Castellaneta (an actor on "Tracy Ullman") provided the voice. It was the "low" voice you referenced in the early shows. This was probably just the voice he came up with as he thought it was a one off. As far as the "why" - there are probably two elements...

1. It is very difficult for a voice actor to maintain a voice characterization constantly over 25-30 years.
2. You'll notice it is easier for Homer to emote and be sarcastic with his newer voice.

For question 2) According to the link below, the change was gradual - but it seems like it is most pronounced with the end of season four to the beginning of season five.

See: http://www.nohomers.net/showthread.php?89821-Homers-voice-changes ... if you watch an episode from today, versus one from 1989 - you'll notice great changes in all of the characters.