control access to document management mailbox for non company users

Easiest way to achieve this would be with a distribution list. You add the external users as contacts on your exchange so that they can be added to the distribution list and assign the distribution list an email address so that it can be used externally. At least this way everyone just manages their inbox and no one will have to manage an additional mailbox which always results in more problems than it solves.

so everyone would have to login using the 1 email address and password?

Users would just login to their usual mailbox, think of the distribution list as a virtual mailbox. Exchange receives an email addressed to the distribution list and then sends a copy of the email to each email address specified in the distribution list.

but im not realy using this for receiving email
im going to use it as a store location for email
so create a public fodler called company jobs then sub folders for each job name
give all users access and they will just file in the email to the correct folder

i need a email storage location to store and manage emails
 i need to share this location between my company employees and other external company employees tat will be working on the project
 i was thinking of using either a mailbox or a public folder

Either one would work. But possibly a Shared Mailbox would be the best way to go.

how can i control access to this for my users and external users

You'd need to give them a user account with a mailbox. You can then grant access to the Shared Mailbox by either assigning Full Mailbox Access, or, Add-MailboxFolderPermissions for specific folders within that Shared Mailbox.

can external non company users have multiple exchange accounts (their own company and mine) configured in outlook

Yes. In Outlook 2013 you can configure multiple Exchange accounts under one profile. In older versions of Outlook you would need to create separate profiles in Outlook.

how can i manage access and security

I mentioned folder and full access permissions above. One other option when you create the user is to also create a dummy group called "No Access". Assign this as the primary group and then remove the "Domain Users" group. Don't assign "No Access" anywhere. That way they can't do anything other than access this mailbox. You could also restrict access via Outlook AnyWhere or ActiveSync. Force them only access via Outlook Web App. Might be one option. Access through Outlook Web App would also remove the requirement of two Exchange accounts via Outlook.

A great collaboration tool you may also want to look at is SharePoint. Designed for collaboration. Especially with outside parties as well.

how can i access a shared mailbox on android and iphone
is tere a difference between shared mailbox and a user mailbox acting as a shared apart from shared not having a username and password
at least with a user mailbox acting as a shared it would have a username and password which could be used to setup the account on mobile devices