I earned a $0.01 dividend on a stock i purchased through cashapp. Cashapp is not on the list of supported banks fpr turbo tax. It will not let me put in the info manually.

The IRS allows you to round income items of less than 50 cents to zero dollars.  Since your dividend was only one penny, this would round down to zero dollars and you would not need to report it.  

I earned a $.53 foreign dividend on a stock i purchased. Do i need to enter it?

How was this dividend reported to you and was it denominated in $US?