Don't keep activities - What is it for?

I believe it's a feature used for debugging purpose.

From the Titanium doc:

Don't keep activities under the Developer Options menu. When this option is enabled, the Android OS will destroy an activity as soon as it is stopped. It is intended to help developers debug their apps. For example, it can simulate the case that Android will kill an activity in the background due to memory pressure. In normal use, it is not recommended to turn this option on because this may lead to unexpected issues on the apps, such as freezes, force closes and reboots.

It sounds like it basically helps testing deterministically how your app behaves when the OS shuts it down due to any reason (out of memory and so on).

So, this replied to point 1. Point 2 is: Yes, I guess :)

EDIT: further references

• On SO How to know "Don't keep activities" is enabled in ICS?
• an interesting thread about that on androidcentral (reply from MagouyaWare)

The Android framework may destroy your activity any time it's in the background or backstack, and you should write your activities so they behave correctly when this happens. Exactly what that entails varies depending on what the activity does, but it generally includes implementing onSaveInstanceState(...) and restoring any previous state in onCreate(...).

The "don't keep activities" developer option simply changes the framework's behavior so it will always destroy your activity when it goes into the background or backstack. This allows you to test how your activity responds to what is normally a rare occurrence.

A link cited in another answer says:

In normal use, it is not recommended to turn this option on because this may lead to unexpected issues on the apps, such as freezes, force closes and reboots.

This is incorrect. If your activities are written properly, the only effect of having "don't keep activities" turned on should be (possibly) slightly higher battery and CPU usage from constantly saving and restoring persistent state. Any apps that exhibit "unexpected issues" or force closes when this option is on are broken and need to be fixed. As a developer, I habitually leave "don't keep activities" turned on all the time. I've seen a lot of buggy apps, even some of Google's own. But it's never caused a reboot, and I don't think there's any way it could.