Can the wallet's balance be deduces from the wallet's address and the blockchain's history? Is this concealable? Since all bitcoin transactions are public, I guess that all transactions could be summed up to get any wallet's balance. Thus sharing a wallet's address means sharing the whole wallet's data. Even using a proxy wallet would not hide the pattern of expenditure thus potentially revealing where the Bitcoins are being spent. Is there a way to be able to receive payments in Bitcoin, yet keep the balance concealed?
Looks like you misunderstood what is the wallet  and the address. Wallet is not an address, wallet is a bunch of addresses. 

An address is a single-use token

Addresses are not wallets, and do not carry balances.


  Thus sharing a wallet's address means sharing the whole wallet's data.


Addresses in this particular wallet doesn't related each other, therefore if you know one address you can't calculate the balance of all wallet.