[Ethereum] How to transfer balance to another address? w/o syncing with network

No.

You cannot send the entire balance because the fees are deducted from your account's balance, not from the value being sent. To sweep an account you need to send balance-gas*price ETH as the value, and also manually set the gas and gasPrice to ensure that you exactly zero your account.

E.g. If you have 5ETH and want to sweep it:

• A plain account-to-account transaction costs 21000 gas
• The current minimum gas price in the network is 20 GWei
• Set value to 5ETH - 21000*20GWei = 5ETH - 42K GWei = 4.999958ETH

Contracts are limited to sending funds actually "in" the contract and there is no way to program a contract to spend from another wallet.

Try this.

pragma solidity ^0.4.21;

contract PiggyBank {

    address public owner;

    event LogDeposit(address sender, uint amount);
    event LogWithdrawal(address sender, uint amount);

    function PiggyBank() public {
        owner = msg.sender; // only the owner will be permitted to withdraw funds
    }

    function deposit() public payable returns(bool success) {
        emit LogDeposit(msg.sender, msg.value);
        return true;
    }

    /**
     * This is NOT needed, but for learning purposes, a convenience ... 
     * Anyone can check the balance at any address at any time, without this assistance.
     */
    function getBalance() public view returns(uint balance) {
        return address(this).balance;
    }

    function withdraw(uint amount) public returns(bool success) {
        require(msg.sender==owner);
        emit LogWithdrawal(msg.sender, amount);
        msg.sender.transfer(amount);
        return true;
    }

}

Hope it helps.