The safest thing you can do with a cell phone is not have a cell phone. Having a mobile device means that at least your cell phone provider and more than likely the company that makes your OS know where you are at any given time. If you're going to do something you don't want people to know about, leave your phone at home. It is entirely possible to live without a cell phone, but it's okay to have one. Just make sure you use it responsibly and sparingly, and don't use it when you don't have to.
Your Existing Device
The best place to get phone applications is through F-Droid on android and it's many available repositories. F-Droid is a Google Play store replacement that only carries Free and Open Source (FOSS) software. There you can get applications such as replacements for existing proprietary apps on your phone such as NewPipe (for YouTube) along with automatic and easy updates.
Many of the same web browsing tips that are in the above Web Browsing section are valid for mobile web browsing. Firefox mobile even supports browser extensions, to improve your tracking protection. However, a few other browsers are worth using on mobile. Bromite and Vanadium (bundled with GrapheneOS) are security focused web browsers based off of Chromium along with some additional features such as a native ad blocker and DoT support. There no calls to google or anyone sent in these browsers despite popular belief. Firefox Klar is a version of Firefox Focus (a self-erasing, privacy-focused browser) with some extra tracking protection. Also, Tor Browser for android is excellent if you require strong anonymity.
Outside of Apple's iMessage, most systems leave messages encrypted by default, leaving them especially vulnerable to MiTM attacks. One remedy (but not cure) to this is to use an end-to-end encrypted messenger such as Signal, Session, or Wire. All of these messengers can also be used to place secure calls and video chats.
If you're on an Android device and feeling adventurous, installing LineageOS is a good choice to minimize Google's tapping of your phone. If you can get your hands on a Google Pixel, consider GrapheneOS, a continuation of CopperheadOS. GrapheneOS is a security orientated distribution of AOSP with [numerous privacy and security features].(https://grapheneos.org/usage) not present in most operating systems (even GNU/Linux). Note that these will restrict you to F-Droid unless you add Google apps back in- but what's the point then, anyway?
There is not much you can do due to the restrictive nature of iPhones.