To install from sdcard you need a file manager, if you don't have one you can get one from play store I use es file manager. Open file manager navigate to .apk then click it you will be asked if you want to install, click install apk will install.
As far as lost apps, sign into play store at top right press the arrow pointing down with line under it. Then next screen top left press the word all. This will show every app ever installed on any device via current logged in Google account.