Hi Wendy,
This is a lengthy post due to the detail I've gone into. You've expressed a desire to learn, hence the detail. Take it slowly, Note that some of this is based on my interpretation of the formulas as they appear in the screenshots. As mentioned below, I don't have or use an iOS device, so I'm unable to test what I've written below. Let me know how what I've said fits in with your observations.
B
Just saw your screen shots, with SG's formula and mine.

The Syntax error is the missing parenthesis after A5 (and the extra one at the end of the formula).
Should be: =IF(AND(DUR2HOURS(A5)<48,O5=FALSE),"*","")
With that corrected, you'll get another error message regarding DUR2HOURS. This function changes a Duration value to a number representing the number of hours equivalent to that duration. Cell A5 contains a Date and Time value, not a duration, and the function will return an error message, "The function DUR2HOURS expects a duration, but cell A5 contains a date."
Revise the formula to read: =IF(AND(DUR2HOURS(NOW()-A5)<48,O5=FALSE),"*","")
Regarding the second example:

Copying the formula as it appears, I see several errors and possible errors.
=IFERROR(IF(LEN(ISBLANK(O8)),""*"",IF(NOW, "" ()-A8<DURATION((,2),""*",""")),""""),)),)
iOS appears to show an opening parenthesis— ( —using the concave end of a function name if it is to contain the argument(s) for the function, and as 'crescent moons' when they do not directly follow a function name (no examples in this formula). Closing parentheses— ) — are always shown as 'crescent moons.'
Any parentheses that display as ordinary type ( such as those enclosing ',2' after DURATION) are either intended to be text, or are placed in error.
Functions that take no argument, such as NOW, display with convex curves at both ends, suggesting that while parentheses are required after these functions in OS X, they are not needed (and likely not allowed) in iOS.
LEN(ISBLANK(O8))
ISBLANK(O8) looks at cell O8, and if it is blank (empty), returns TRUE, or if it contains anything, returns FALSE. A checkbox cell is never empty; if checked, it contains TRUE, if unchecked, it contains FALSE. ISBLANK will always return FALSE. LEN measures the length in characters of whatever is in its parentheses—in this case FALSE, so it will always return 5.
If testing a checkbox, it's sufficient to use only the cell address of the checkbox, then arrange the 'do-if-true' and 'do-if-false' arguments to suit (checked=TRUE, unchecked=FALSE).
The white lozenges in the formula contain text strings. I am guessing they are generated by tapping the "abc" button visible in the screen shot, and that tapping the button inserts the lozenge with a pair of double quotes already included. Only the text that you want to appear should go between those quotation marks. Most of these lozenges appear to have an extra pair of double quotes.
Commas are used to separate arguments in a function. Their placing is critical.
Here is a revision of the formula shown above. I don't use an iOS device, so I am unable to test it. Remember that all of the left parentheses - ( - will be added automatically, and will display as concave right ends on the boxes containing the function names.
=IFERROR(IF(O8,"",IF(NOW-A8<DURATION(,2),"*","")),"")
In English:
If O8 is checked (TRUE), this cell will appear empty; otherwise...
If the date & time in A8 is less than two days earlier than NOW, this cell will show an asterisk; otherwise...
This cell will appear empty.
If any of these steps generates an Error*, this cell will appear empty.
*Comparing NOW-0 to a duration will generate an error until there is a date and time vaue in A8. IFERROR is used to trap this error.
Regards,
Barry