IF cell is between % AND % return text + IF another...

Your formula isn't telling it what to do if the condition is outside of those values. it should be something like =IF(AND(AA5>10%,AA5<19.999%),"C", something else)

Here is an alternative because I only addressed the first part of your question but not the second part...
=LOOKUP(AA5,{0,0.1,0.2,0.3},{"D","C","B","A"})

You want nested IF statements:

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...which returns the same as the LOOKUP formula in post#4

The tests are done sequentially, so testing for higher values is only done if lower values were not found. This eliminates the need for AND statements with two criteria each.

well this would be the "consolidation" of those formulas, I would reorder it to this...
=IF(A1155>=30%,"A",IF(AND(AA5>20%,AA5<29.999%),"B",IF(AND(AA5>10%,AA5<19.999%),"C",IF(AA5<10%,"D"))))
but it will produce D as a result even if the cell is blank. You might want to proceed the formula with IF(AA5="","" then follow it with the rest.
and my lookup formula is easier and shortens the IF / then formula.

EDIT: oh, and leelnich's formula is also cleaner and simpler than yours too.

EDIT2: goes to show you what just trying to answer the question does, I should've known to give you the simpler version that leelnich gave you in post #6 as I know that you don't need the AND statements in between. Sheesh! Good one leelnich!