Can the printout of E-aadhar i.e the softcopy of your original aadhar card be used for official purposes such as opening a bank account?

Yes print out of e-aadhar is equally valid like original aadhar card. You can ceheck the steps here to link the bank account with aadhar card:There are two ways to link Aadhar Card to Bank account online: (Online method) Add details of Aadhar to your bank account via the net banking portal of your bank. (Offline method) Add details of Aadhar to your bank account by submitting a form to your bank. You can download this form either from your bank’s website or visit the nearest branch of your bank and ask for the Aadhar to Bank Account Seeding Form. As time flies by, I would suggest that since the Option 1, net banking is less time consuming than filling up the form and submitting it to the bank, I suggest you to go with Option 1. Having said that, if you do not have Net Banking enabled in your bank account, you are left with Option 2 only.If you already have net banking enabled for your bank account, proceed further to link Aadhar to bank account: Now you need to login into your net banking account. Once you are logged in, you will find the option or link as ‘Update Aadhar Card Details’or ‘Aadhar Card Seeding’. Now click the link to open the other page Now bank will ask for some basic information about your Aadhar Card. Enter the details required details correctly. After entering the details submit this information by hitting the Submit Button. Once you submit the details, it will be saved to the respective bank database. After that, bank will verify the information the details of your Aadhar (http://uidai.gov.in/) and link the Aadhar to your bank account. You would be informed or notified either through email or SMS to your registered email address or phone number once this process is completed. Also National Payments Corporation of India (NPCI) has provided the facility to check Aadhar- bank account linkage by dialing *99*99# on mobile phones at the cost of Rs. 1.50 per enquiry. So, these were the simple and easier steps through which one can link Aadhar to bank account online. We hope this article will help you link your Aadhar to your bank account – do note that it is also called as Aadhar Bank Account Seeding  or Aadhar Seeding.

I am a retailer of recharge cards. As far as activating new sim cards is concerned, the telecom companies dont accept downloaded aadhar cards. The reason they state is those e-aadhar cards do not have father's name field on them(just above the address, there is s/o field only). So I dont think the downloaded aadhar cards can be used everywhere.

you  can download AADHAAR card duplicate copy through UIDAI official website  .This copy is same as original aadhar card .This downloaded AADHAAR Card will be accepted as a valid ID and residential proof wherever AADHAAR Card is accepted. http://aadharcardupdates.blogspot.in/2015/06/download-aadhar-card.html