I have BTC public address and privatekey with balance. Can I Transfer the balance for another address?
Yes, but first u need import your private key in wallet app, fews mobile apps support this feature, blockchain.info wallet (https://itunes.apple.com/br/app/blockchain-wallet-bitcoin/id493253309?mt=8) is the only that i know,under menu/address/+ (plus button). This will open your camera to scan your QRCode private key in WIF format (51 characters).
In case you dont have private key QR code, can use something to genarate a QRCode, prefer audited and offline code, for example: (https://raw.githack.com/EquestrianBit/equestrianbitpaperwallet/master/index.html), in menu "2. print front"\"my own key", before put yout private key, turn pc offline, only for security questions. All code run local in browser. After get your QR Code, have attention to recommendations in: (How do I send Bitcoin in paper wallet to other person?), like @ugam-kamat told.