You can easily invite members to your workspace from the left side bar at the bottom. Just click on the 'Invite Members' to get started. You can also edit the user access and roles within the workspace settings. Click on the carrot by your name and then 'Workspace Settings' button to get started.

Can users invite team members? Does it show the right status for those invited team members (pending or not)?

Yes. You can invite team members to your workspace. Once they've been invited and accepted, they will have the same access as all other team members. The status of those invited team members will be "pending" until they accept the invitation.