Exchange and Sharepoint provides tools; you customize them for your needs. You might think that these needs are universal and indeed they are but you'd be surprised how much they vary between organizations so your config is likely different than others. What you are really doing is mapping business processes to the technology and that can really only be done by you. You need to figure out what your users need and build a solution that works for them. This probably explains why you aren't finding docs for exactly what you want.
Public folders are viable for Exchange 2010 and for who knows how long. Microsoft initially tried to kill them off but there was a lot of backlash so they've backed off on that a bit. If you're not already using them, you'd be wise to skip them and find a solution that uses mailboxes or Sharepoint instead.
Really your 2 options are as you've mentioned: use a mailbox and give everyone access or use a Sharepoint site. Either can work. You don't mention if you already have Sharepoint or not. If you don't, it isn't an insignificant thing to build so I'd recommend sticking with your mailbox approach which is a common solution. Obviously you need to address your issues with the permissions problems but if that's your only issue, I'd simply focus on that specific technical problem and find a solution.
I wouldn't obsess over that comment in the Microsoft doc about using resource mailboxes or Sharepoint for collaboration. A resource mailbox wouldn't be appropriate for your specific use though Sharepoint might be.
Each Exchange server with the Mailbox role installed can have one or more mailbox databases, so if you only need to split your database load, you will need to create a mailbox database on the new server and move some mailboxes to it; end of the story. Of course, this means that if a user has a mailbox on ServerA and ServerA goes down, there will be no fault tolerance; users whose mailboxes are on ServerB will be fine, but users with mailboxes on ServerA will not be able to access them.
If you want redundancy, you will need a Database Availability Group; in a DAG, each mailbox database has one or more copies on different servers, only one of which is active at a given moment; if the server where the active copy of a mailbox database resides goes down, another copy will be made active and users will be automatically redirected to it. The down side of this is, you will at least need twice the disk space (because each database will have at least two copies), and some processing power of your servers will be used for data replication.
You also need to take into account that Exchange is not only made by mailbox databases: in order for it to work, you will also need at least an operational server for each of the two other main roles, Hub Transport and Client Access. Hub Transport servers are automatically load balanced and redundant, so you will only need to install the role on the new server and everything will be fine. The same is not true for Client Access: other than installing the role, you will also need to create a Client Access Array in a load-balanced configuration, which needs to be handled at the IP level. Ordinarily you could to that using Windows' built-in Network Load Balancing service, but there's a caveat specific to a two-servers scenario like yours: a Database Availability Group relies on Failover clustering, which is not compatible with Network Load Balancing.
The end result of this is, if you want a fully-redundant setup, you will need two multi-role (Mailbox, Hub Transport, Client Access) servers, a Database Availability Group, a Client Access Array, and an external hardware load balancer, without which you would need to either give up redundancy for the databases or for the Client Access role.
Best Answer
This simply means that a mailbox move request exists for that user. If you expand "Recipient Configuration" you will see an item called "Move Request". Click on it to view all the existing move requests and their status. If they are all successful you can select all and clear them. That will make the green arrow go away.
Or if you like the EMS:
to view all the move reqests.
to clear a specific move request.
to clear all move requests.