Using Spotlight to find things on my iPhone and iPad is the easiest way for me to navigate through apps, mail and contacts. It’s been my go to way of doing things for a long time. Simply swiping down from will reveal the Spotlight search box.
Spotlight

Spotlight also makes it really easy to find all the apps on your devices. By simply searching for a “.” it will bring up a list of all your apps.
Spotlight Search

After a quick test it seems you can use most keyboard symbols or punctuation marks to get the same results.
Spotlight Search

To find apps that you have previously installed on your devices open the App Store app. On the iPhone go to Updates – Purchased. You have the options of All and Not on This Phone. Pull down the screen to reveal the search box.
Purchased App Seacrh iPhone

On the iPad the Purchased option is at the bottom of the screen. Select this and then you have the same options of All or Not on This iPad. You also have another option to view iPad Apps or iPhone Apps.
Purchased App Search iPad