How can I handle when header color is White? Because text color is also white, we cannot see the items in the status bar.

Android 5.0, We are able to change only status bar color not status bar text color. Android Lollipop Set Status Bar Text Color
If you use API 23, There's a solution here. API 23 status bar color is White
I'm not sure. Can it work perfectly in ionic? I can't give a solution to you. I need to know more and do more testing. If you find the solution, I'm happy to accept a pull request.

Can we use your option for Android and native status bar plugin for iOS devices on the same project?

Of course.
I can answer your question now. A pr merged: Platform separately: Each platform does not affect each other.
I did some work to make all the code only act on android platform. The code is harmless!
E.g:

// src/app/app.component.ts
if (this.platform.is('android')) {
	this.statusBar.backgroundColorByHexString("#33000000");
}

/* src/app/app.scss */
.platform-android {
  page-home, page-language-details {
    @extend %super-bar;
  }
}

I use this.platform.is('android') and .platform-android selector to get information about current device. So that the code only acts on android device. More information, please check the source code.
Are you satisfied with these answers?😀

Thanks a lot @jeneser
I'll try to implement your solution later today and will let you know if I'll have any issues.