[Sony Xperia XZ1 Compact Guides, News, & Discussion] mhaha:
Alternative implementation that I use: Add a toggle on the home screen to quickly switch between Ring/Vibrate/Silent modes

First install Media-Mute [free & ad-free]. What this app does is automatically mute the media volume whenever the ringer volume is also muted, which applies to both Vibrate mode and Silent mode.

For some reason, since Android 4.x Google has decided that Silent mode should only apply to the ringer, instead of silencing everything that can make sounds out of the speaker. Media-Mute fixes that.

Next, install Silent Mode Toggle [free & ad-free], then add the widget on the home screen. Switching modes is now super easy, just tap on the toggle.

What I really appreciate about this app is that it allows customization to the toggle order. For example, I never use the vibrate mode, so I can set it to toggle between Ringer > Silent only.

As a bonus, it also lets you use your own custom icons for the toggle, super cool and makes it possible to perfectly complement your home screen layout.

Hide the annoying "running in the background" notification that comes with Android 8.0

With Android 8.0 Oreo, Google thought it would be a great idea to permanently remind you of any background processing currently running in the form of an impossible to dismiss notification.

While the intention was well meaning, the execution leaves a lot to be desired.

Thankfully, there's an app for that! Just install this cleverly named app Hide "running in the background" Notification [free & ad-free], problem solved!

Vibrate phone when call connects, ends

Yet another app to the rescue! VibCall [free & ad-free] brings this useful feature found on some OEM phones to any compatible Android device.

Basically, your phone will vibrate once to let you know that a call has connected, and twice when a call has ended. It's something that once you've used, you wonder why it's not baked into the Android system as a default option.

Add a fingerprint (Smart Lock) compatible screen lock toggle on the home screen

So Sony has unilaterally decided to remove double tap to sleep feature with no sign of bring it back. But I still want to turn off the screen and lock the device by tapping on the screen instead of waiting for the system to hibernate or hitting the power button.

The OP listed a paid solution which brings back double tap to sleep, but for those looking for a free alternative, this is the solution I'm currently using - Smart Screen Lock Pro [free & ad-free].

It's not a double tap anywhere convenience, but a toggle that is better than nothing, and most importantly it's compatible with fingerprint unlock. I've tried numerous screen off apps in the Play store, and this is the only one that I was satisfied with.

IMPORTANT: Take the time to carefully read and follow setup instructions, it's necessary for it to work properly due to OS restrictions. Once it's setup correctly, simply add a shortcut on the home screen and tap it to lock.

It's worth mentioning that it's not a true "instant" screen off and lock, but without root this is probably the best solution we'll get.

Non-root ad blocking

Ads are a necessary evil for the current economics of the Internet, but aside from the annoyance factor, they eat up precious mobile data, plus there's also very real security risks with ad networks, potentially hogging your phone's resources and draining the battery.

Whatever the argument, if you do decide to block ads, there are quite a lot of ad blockers to choose from.

Personally, I use dns66 [free & ad-free]. In my experience, it's very lightweight, and I haven't seen any ads in my browser or apps.

It does have its quirks though, sometimes downloads fail, such as OTA update or file in browser, for one reason or another (the author says it's a bug with the Android OS itself, see linked post).

But it's easy to workaround, just temporarily disable dns66 by tapping pause on the notification, and download again. After download has completed, tap the notification again to resume.

By the way, this is also the main reason I installed the hide background notification app.