App Store sometimes can't install, iCloud icon instead of INSTALL icon
The cloud symbol means that the app is associated with your account and has been previously installed using your Apple ID (on any of your devices). If you tap on it the app should start to download to your phone.

You may be prompted for your Apple ID password though. If so, without the password you'd be unable to install apps whether they are associated your account already or not.

If so you can go to the link below to try to recover your Apple ID password.

http://iforgot.apple.com