I installed the langhans Dogecoin Wallet on my android device and backed up my private keys. Is it sufficient to backup the wallet to avert loss in case of loss of or damage to the phone?
The private keys are the critical thing and are in the wallet backup. They're what is needed to transfer coins. If they become public (i.e. stolen), whoever has them can transfer your coins to themselves. If you lose/forget your private keys, you can't make transfers, the coins are worthless to you, effectively lost.
You can create multiple addresses for bookkeeping. For example you can create an address for client X and an address for client Y, your wallet will show how much each address has received. Also, creating a new address for every transaction can somewhat anonymize the transactions.
If you already possessed some Dogecoins before the backup, restore it on another device and verify the amount displayed is the same. Else, get some coins, backup again and try restoring it elsewhere.
What exactly have you read about max. amount of addresses? Theoretically you can have as many addresses as you wish, though in practice the performance of the wallet will degrade the more addresses you have - the exchange Cryptsy was bitten recently by this and they had to create another wallet.
The point of having multiple addresses, in Dogecoin as in every other crypto-coin, is to be able to more easily track who payed you: you can have one address to receive payments for your services, another for the goods you sell, yet other one for tips you may collect (from Reddit, or a blog or whatever), the coins you mine, the ones you buy, etc. Most vendors actually generate a new address for each customer to be able to easily tell each payment's origin appart, some even use a new one for each transaction.