Hey man, so hopefully I can address some of the concerns you're having. First of all, you're correct in that Proving Grounds as-is is not a faithful representation of classic ARAM gameplay. We took elements of what we enjoyed from both ARAM and ARAB and adapted them to an existing map; the result is that it's something that's similar, but still quite different, but what we hope is an improvement from ARAM and ARAB.
To address your concerns piecemeal, I'm going to refer to Proving Grounds as PG, classic ARAM as ARAM, and ARAB on Dominion as ARAB. Some of the justifications have already been covered by the other posters, so I'll focus on what's not been mentioned.
Health relics, along with brush, are both elements intended to give the otherwise straightforward terrain of Proving Grounds some deeper gameplay. On ARAM, there's the notion of two distinct fronts. You've got purple team in a line parallel to blue, and this is the default configuration until someone initiates or gets caught. While there's certainly merit to this gameplay, it does marginalize the usefulness of melee champs and amplifies the effectiveness of ranged pokers and AoE champs (say, Xerath and Ashe respectively). What we did on PG is break these fronts; you've got champs vying for brush control and scrambling for health relics. It's an ongoing process that keeps the state of both teams quite volatile and provides a lot of openings to capitalize on mistakes.
Increased Starting Gold
This was a decision made very early in the project, and it directly relates to the melee/ranged disparity and the general feeling players have when they're "stuck" in battle. To clarify on this, it's when you're low health with no sustain; too low to properly fight, but you don't want to feed your opponents a free kill. Increased starting gold gives players the ability purchase enough sustain or survivability to mitigate this issue, though not enough to solve it. In addition, it allows for a much higher variety in starting builds.
I actually have to go do something right now, but I'll be back to answer the rest of the points. Please note that we do plan to support Proving Grounds; both Brackhar and I will be providing short term support, and I'll actually be jumping onto the live team for the conceivable future to provide long-term support for not just Proving Grounds, but other non-SR maps as well. It's also possible that we add a "classic" mode to the map in the future that removes the health relics, ambient gold and experience, and sets you back to level 1. But for now, I (and the PG team) implore you to play the map as-is and give us your feedback.
Alright, continuing on.
Starting at LVL 3 and Passive Experience
Starting at level 3 was specifically added to address the issue of--you guessed it--melee/range disparity. Starting at level 3 address the problem two-fold. First, on ARAM, melee are hindered for the first few levels due their core design; oftentimes their primary damage ability or crowd control is on a separate ability from their mobility skill. This means that unlike ranged AD or casters, they're effectively unable to participate in battle until they gain both their mobility and primary damage. Second, fighter (and many other melee) design involves the use of three abilities to create a combat loop. Renekton, Riven, Tryndamere, and Pantheon are great archetypes here; compare this to a Xerath who can effectively operate with one or two spells, or Ashe whose biggest impact comes from repeated use of one ability. Passive experience is there to address the snowball factor; unlike Summoner's Rift, Dominion, or even Twisted Treeline, the majority of battles on ARAM/B/PG involve and impact all champions on a team, which means that if an opposing player is taken down, the entire team snowballs, not just the individual. The passive experience gain is there to offset this snowballing, and also to push the pace and try to keep overall game time down.
Wide-open lanes are advantageous for AD carries and long-ranged champions. Narrow lanes are advantageous for melee. PG is more narrow than Summoner's Rift, but it's not quite claustrophobic. We experimented with more open layouts but they were very punishing to melee. As you've gathered by now, the ranged/melee disparity was a big factor in why we made the changes we did. I made another (shorter) post on the subject here: http://na.leagueoflegends.com/board/...84043#25184043
Items are a mix between Classic and Dominion. Bloodthirster was replaced with Sanguine Blade because the stacking nature of BT led it to generally snowball too hard. Wriggle's Lantern was disabled because the attached Ward removed Brush gameplay. We're open to replacing it with a similar item though. Madred's Bloodrazor was replaced with Kitae's Bloodrazor because Madred's was inadequate as a counter item given its price point.