Is an Antec Basiq BP350 350W ATX12V v2.01 Power Supply compatible with a Dell Dimension E521?

It will work but I would suggest stepping forward to the Antec Basiq 430W unit. Will run cooler with a little extra pump to spare. This way you will not run on the edge. I have installed these in many smaller system with very good results. Mini tower refers to a short in height of the case. If "S" is not designated in the model name than the power supply is a standard ATX unit. I did look this up at Dell. The other source you listed, I would not. Antec has been around a long time and has a very good reputation. They stand behind their products. Newegg will take care of you also. 80% of the hardware I use for systems comes from them. I use Antec and Corsair in my own systems. (6). Hope it helps.