[SalesForce] How to Update Logo of Managed Package App

Yes we've done this and been successful.

However your correct to be cautious about it though. We've had things go wrong under the hood in the past (typically with more complex dependencies than your describing here though). So long as you're not under major pressure to release Salesforce support have in our experience been able to pick through things for you and sort things out, just be sure not go messing around further if things appear odd.

Uninstalling from Packaging Org. So long as you no longer have any references to it, it will uninstall as normal, even from a packaging org. If however you've made references to it via fields lookups for example, that you cannot remove or edit out from your package, because those have been released you will not be able to break the dependency. This doesn't mean you cannot install the unmanaged version, as this will be in the your packaging org namespace. Its just that it would look a little odd to admins in your subscriber orgs to see the same classes, objects etc from the Action Plan namespace and your package namespace, other than this urglyness that may be tolerable.

Uninstalling from Subscriber Org. This again will be possible once you the subscriber org has upgraded to your new dependency free version of your main package.

Installing beta package releases into production orgs is not possible except in very special cases (the "production" orgs created via the partner portal), so the answer to your first question is almost always no.

For your second question, you can bypass the appexchange if you want, and distribute your app directly via it's install link, certainly. If you don't go through security review some benefits of being a managed app are witheld however. For example, if you go through security review tabs in your app don't count against the customer's tab limit for their org, but if you skip the review they do count.

You can still use the license management app with a non-reviewed application by creating a private appexchange listing and using that to manage the license settings, however going through security review is recommended of course.

Push upgrades are only available to apps that have undergone security review, and once that's done have to be enabled by salesforce support for your dev org.