Marita, you don't need a Portuguese address to open a Portuguese bank account. You do need proof of address of your foreign address, though, like a bank statement or ID card with your address on it.
If you live less than 183 days per year in Portugal, you do not pay tax in Portugal.
Your realtor/agency depends on where you choose to live, as there is no central database for all properties in Portugal. Instead, they are listed by the agency who is commissioned by the seller. What you need to do is to choose the area first, then search for the properties available in that area in the inventory held by different agencies or in a property website like imovirtual.pt
It's a lot more work to do it this way, but it's worth using the property websites as there are also properties listed there by the owners who prefer not to deal with agents.
I'm a Canadian living in Porto since 2013. Message me if you want to know more.