The maximum number of heart containers I can have

As far as I can tell, the bird statues are the only way to save. This article mentions save points in dungeons, and I am assuming they are refering to the bird statues as well.

There are save points scattered throughout the adventure, even in the middle of dungeons. This might sound like an obvious improvement, but it will be taken as something approaching heresy by the more traditionalist of Zelda fans. If you die, you can continue at the last save point with all of the items you've found. Nintendo clearly wants players of all skill levels to be able to finish the adventure.

You can only buy 3 extra wallets from Beedle, each with a capacity of 300 rupees giving you an additional capacity of 900 rupees.

The largest wallet that I was able to obtain was the Giant Wallet which you get from one of the special quests.

You get it from Batreaux after giving him 50 Gratitude Crystals.

That gives you a base capacity of 5000 rupees for a grand total of 5900 rupees when you include the extra wallets.

There is an even larger wallet, the Tycoon Wallet which gives you a base capacity of 9000 rupees bringing you to a grand total of 9900 rupees carryable max.

You get it from Batreaux after giving him 80 Gratitude Crystals.