If I already connect a bank or card account to QB and I connect the second time, will it download same transactions twice and show duplicate transactions in my book?

Yes, it will cause a duplicate, kendocircle. 
 

We can exclude the duplicate transactions showing up in your bank feed. This is to remove them from your books permanently. 

1. Go to the Banking menu from the left navigation panel.
2. Choose the Banking tab, and choose the account you want to use.
3. Click the For Review tab.
4. Mark the checkbox of the transactions you want to exclude.
5. Select the Exclude option. 
6. The items will be moved to the Excluded section.
7. From the Excluded tab, place a check in the box for the transaction you'd like to permanently delete.
8. Tap the Delete tab.

For more insights about the process, please check out this article: Exclude a bank transaction you downloaded into QuickBooks Online.

Additionally, here are some resources you can use to help you in managing downloaded transactions in QuickBooks:

• Categorize and match online bank transactions
• Reconcile an account

Keep us posted if you have further questions about duplicate transactions in QuickBooks Online. We're always here to help. Take care and have a nice day!