How can I access iCloud.com from an android device when I don't have access to any Apple device? I need to access iCloud mail from my Android phone.

Many apps are around for this, but they all require some app specific password generated by Apple. To generate such passwords, two factor authentication needs to be enabled on the Apple account. To enable that, one needs an actual physical Apple device logged into the iCloud account. I no longer have any Apple devices.

I also find that I can get into icloud.com using various desktop modes of Android browsers. However, when I try to click on an email to read it, iCloud seems to somehow realize that it's not mouse input. It doesn't respond to my touches. I've tried several different browsers.

I don't mind a clumsy experience, I just wanna access the email somehow. I don't use iCloud email any more, but I just need to access it now. And I don't have any real desktop computer, just my phone.

I've even tried this Debian nonroot app to run a full desktop version of Firefox, but somehow it won't boot on my Galaxy S5 running Marshmallow.
You can use the email app that comes with your phone to access your iCloud account.

1.Open the Email app and tap the menu button in the top-right corner. (If you’ve never used the Email app before, just open it and go to step #3.)


Tap Add Account.
Enter your iCloud e-mail address and password, then tap Next.
Select IMAP and tap Next.
When you see the Incoming Server Settings page, remove the “@icloud.com” from your username.
Change the IMAP server to “imap.mail.me.com.”
Set the security field to SSL/TLS (Accept all certificates).
Make sure the port is set to 993, then tap Next.
On the Outgoing Server Settings page, change the SMTP server to “smtp.mail.me.com.”
Change the security setting to STARTTLS and make sure the port is set to 587 and “Require sign-in” is checked.
Tap Next to complete the process.


Once you’ve gone through this list of steps and saved your changes, you’ll be able to access your iCloud mail via the Email app on your Android phone.

(Source)

Hope this works.