The Samsung Galaxy S5 mini comes with both the stock Android browser (customized by Samsung) and Google's Chrome. Only the stock browser supports Air View.
Anyway, the interfaces of both browsers are virtually identical. Both show favorite web sites on their new tab page and can sync bookmarks and open tabs across devices. The browsers handle multiple tabs (with Incognito mode), but in Chrome you can switch between tabs by horizontal swipes from the side, which is pretty handy.
Air view works in the browser, the first of which lets you simply hover your finger over a web element and it will act like mouse-hover, which is great for websites not optimized for mobile devices.
Note that Chrome has an option to reduce traffic by compressing web pages on Google's servers before they are sent to the device, similar to how Opera's Turbo mode (and Opera Mini) work.
The My Files app organizes your files into categories - Images, Videos, Music, Documents, Downloaded apps, Recent files and even Dropbox files. The My Files app can move, copy, lock and rename files in bulk, even send multiple files to another phone. You can ZIP multiple files to be sent easier.
S Health has a step counter, which is always working in the background, keeping track of how many calories you've burned. For more accurate measurements, the Galaxy S5 mini also features a heart rate monitor.
You just press the tip of your finger against the sensor (below the camera, next to the flash) and in a few seconds you see the reading. For continuous readings, you can pair the phone with a Gear smartwatch or a compatible dedicated sensor made by Samsung, Timex or Garmin (but that beats the point of having it onboard the phone). So essentially, it's more of a gimmicky feature than anything else.
Besides the basic pedometer, S Health can also track running, cycling and hiking. Goals can be set based on distance, time or calories. During an exercise the app can play music and report your progress out load.
A calculator, voice recorder and a memo app are available out of the box.
The Android calendar has been replaced by S Planner (although you can always download Google's stock Calendar). It features six different views: daily, weekly, monthly, yearly, list and tasks. For the month view, events on the selected day are listed in a panel on the right.
The Alarm app is quite advanced too. Each alarm has its own tone, snooze and repeat settings. It also features Smart alarm, which rings quietly, slowly turning the volume up for a less stressful wakeup. The app also features a world clock, stopwatch and a timer. The rudimentary stopwatch and timer are preloaded as well.
Samsung's Apps is now GALAXY apps and has a new design. The layout appears the same and you can find various paid and free apps in the store. The Galaxy Essentials is the best category to look for - it features premium apps that have been designed for or optimized to work with Galaxy smartphones.
Naturally Google's own Play store has its foot in the Galaxy S5 mini door offering the biggest selection of apps available.