tl;dr ⇒ You are using the wrong pattern for parsing

1. Your date String is of the format dd MMM uuuu (a non ISO format) but you are trying to parse it with a DateTimeFormatter.ISO_LOCAL_DATE

2. Your datetime String is of the format MM/dd/uuuu hh:mm:ss a (non ISO) but you are trying to parse it with a DateTimeFormatter.ISO_LOCAL_DATE, which is at least doubly wrong because that formatter tries to parse an ISO date. Your String is non ISO and contains more information (time of day) than this formatter is able to parse.

There are several built-in DateTimeFormatters, like the one you are currently using, but you need to use a correct one or if there is none, create one that covers your String(s) yourself (either by DateTimeFormatter.ofPattern(...) or by using a DateTimeFormatterBuilder).

Here's a small example for your String examples:

fun main(args: Array<String>) {
    // your example Strings
    val dateFirst = "20 Aug 2012"
    val dateSecond = "12/16/2020 12:00:00 AM"
    // you need two different formatters here, your Strings differ in format and content
    val firstFormatter = DateTimeFormatter.ofPattern("dd MMM uuuu", Locale.ENGLISH)
    val secondFormatter = DateTimeFormatter.ofPattern("MM/dd/uuuu hh:mm:ss a", Locale.ENGLISH)
    // then use those according to what you want to parse
    val localDate = LocalDate.parse(dateFirst, firstFormatter)
    val localDateTime = LocalDateTime.parse(dateSecond, secondFormatter)
    // use the built-in formatters for output
    println(localDate.format(DateTimeFormatter.ISO_LOCAL_DATE))
    println(localDateTime.format(DateTimeFormatter.ISO_LOCAL_DATE_TIME))
}

Output (in ISO):

2012-08-20
2020-12-16T00:00:00

Use below to convert the time from String to LocalDateTime, but make sure you are getting the time in String form.

String str = "2016-03-04 11:30";
DateTimeFormatter formatter = DateTimeFormatter.ofPattern("yyyy-MM-dd HH:mm");
LocalDateTime dateTime = LocalDateTime.parse(str, formatter);

Btw, If your String contains seconds as well like "2016-03-04 11:30: 40", then you can change your date time format to yyyy-MM-dd HH:mm:ss" as shown below:

String str = "2016-03-04 11:30: 40";
DateTimeFormatter formatter = DateTimeFormatter.ofPattern("yyyy-MM-dd HH:mm:ss");
LocalDateTime dateTime = LocalDateTime.parse(str, formatter);

One more option:

val formatter = DateTimeFormatter.ofPattern("yyyy-MM-dd['T'HH:mm]")
val dt = formatter.parseBest(str, LocalDateTime::from, LocalDate::from)

Here dt will be instance of LocalDateTime or LocalDate (depending on the str input string).

Note, that you cannot parse input with format "yyyy-MM-dd" into LocalDateTime, even if you use optional parts in the DateTimeFormatter pattern.