What Java DateTime class should I use?

Third question - is there some parser that can parse all the different strings as I listed above? Or do I need to call String.contains() to determine the format and then do an explicit pattern based on that? And if so, using what class?

I might be horrible wrong, but can you use DateTimeFormatter with optional parts on pattern and parseBest method:

List<String> dates = List.of(
    "2019-01-25", 
    "2019-01-25T14:32:23",
    "2019-01-25T14:32:23.12345", 
    "2019-01-25T14:32:23Z", 
    "2019-01-25T14:32:23Z-0500"
);

DateTimeFormatter formatter = DateTimeFormatter.ofPattern(
   "yyyy-MM-dd['T'[HH:mm:ss][.SSSSS]][z][x]"
); // all the possible combinations

dates.forEach( date -> {
            TemporalAccessor accessor = formatter.parseBest(date,                       
       OffsetDateTime::from, // going from most specific date
       LocalDateTime::from, 
       LocalDate::from); // to the less specific 

            System.out.println( accessor.getClass() + " " + accessor);
        }

);

// output for this is 
class java.time.LocalDate 2019-01-25
class java.time.LocalDateTime 2019-01-25T14:32:23
class java.time.LocalDateTime 2019-01-25T14:32:23.123450
class java.time.OffsetDateTime 2019-01-25T14:32:23Z
class java.time.OffsetDateTime 2019-01-25T14:32:23-05:00

As to the 2nd question: Yes there is a "timespan" class in the Java JDK.

For a span-of-time not attached to the timeline:

Period

Represents a number of days/weeks/months/years. Can be used in date calculations, automatically accounting for Daylight Savings Time (DST).

For example, to subtract 3 days from a given date, you could do

ZonedDateTime threeDaysAgo = Period.ofDays(-3).addTo(ZonedDateTime.now());

Duration

Similar to Period but on the scale of days (as 24-hour chunks, not calendar days), hours, minutes, seconds, and fractional second.

ChronoUnit

If you need to do calculations on a wider scale (like include hours/minutes/secods etc) There is also the ChronoUnit enum:

ZonedDateTime threeHoursAgo = ChronoUnit.HOURS.addTo(ZonedDateTime.now(), -3);