Can we have both Helpdesk Manager and Agent addins installed on the same machine?

Yes, you can. Having said that, ideally you would want to have a system with the Helpdesk Manager tool, and the rest (users) with the Helpdesk Agent tool. However, if you have 2 or more admins, you can choose to install the Helpdesk Manager add-in on those systems too. You will also need to install the Agent tool on those systems too if the admin needs to work on the cases in Outlook. It is perfectly fine to have both the manager add-in and the Agent add-in installed on the same system.