Can we have multiple public anonymous access site collections in a tenant
Unfortunately not. You are only allowed to have one public web site collection in Office 365. If you try to add a subsite to your public site, you'll see the text "This site does not have any subsites."
On team sites you can allow sharing with external users who don't need to sign in. In a way, this is anonymous too, but you can't share the entire site collection with a simple link.
Microsoft says the same in there service description; "only one public-facing website per tenancy".
Share Team Site
To share a team site with external users, you need to allow external sharing in Office 365 Admin Center.
Then in the SharePoint Admin Center, you highlight the team site site collection and hit the Sharing button
When sharing is enabled, hit the share button in the upper right corner and start typing your external users e-mail addresses. Select the SharePoint group they should be part of and save.
An e-mail is sent to the external user(s) which signs in with a live-ID or another office 365 account. They don't use their e-mail addresses directly. However (and this is the good part) - any alert is sent to their invitation e-mail address.
When an external user have accepted your invitation you can see them in the SharePoint group you added them to.