What Android device manufacturers supply their devices with longer software update life cycles than Google supplies its Nexus and Pixel devices? Google's software update life cycle policy for Nexus and Pixel devices is that:
1. They "get Android version updates for at least 2 years from when the device became available on the Google Store. After 2 years, we can't guarantee additional updates."
2. They "get security patches for at least 3 years from when the device first became available, or at least 18 months from when the Google Store last sold the device, whichever is longer."
Source: https://support.google.com/nexus/answer/4457705?hl=en

Are there any manufacturers that give their devices longer life cycles than Google gives Nexus and Pixel devices when it comes to Android version updates, security patches, or both?

In addition, if possible, please tell me how rapidly these manufacturers provide Android version updates and/or monthly security updates, in comparison to how rapidly Google provides them to Nexus and Pixel devices.
Everyone worth their salt is 2 and 3 for Security Patches, manufacturers with fewer phones and a greater concern for security (Blackberry) might extend the life cycle for the security but Android Version upgrades won't come if the next version is far enough away to let it slide (depending upon Devices in service vs. the idea of buying a new phone).

Once you're off Contract you can Root and Update yourself (cost the Mfg. nothing too) so there's little reason for them to support older Models IF people aren't going to complain (or make it a purchase consideration).

As for the second question: http://www.androidauthority.com/android-oem-update-speed-743073/ .

For Nougat:

LG: 78 days
Motorola: 88 days
HTC: 95 days
Sony: 99 days
Xiaomi: 126 days
OnePlus: 131 days
Samsung: 143 days
Huawei: Might get Nougat Q2 2017