Can someone tell me whether D-Star and the coordinates can replace position tracking from APRS and/or finding the direction and distance to someone? In other words, can I look someone up on a map using D-Star and the coordinates they are sending?
The purpose of APRS is to provide local, tactical information via RF. In other words, you can use APRS to determine the locations of other stations or objects or to get weather or local information using just amateur radio. All of this information is typically passed using a shared RF frequency per local custom. 144.390 MHz is the frequency used in most of the U.S. APRS digipeaters extend the range of APRS stations much in the same way that voice repeaters extend the range of voice stations.
APRS is linked to the Internet through stations known as I-gates and the APRS-IS which is a world-wide network of linked computers that share the position reports and tactical information received by the I-gates. Internet-based web sites, such as FindU.com and APRS.fi, tap into the APRS-IS servers and display the information received by the I-gates.
Note that most I-gates are one-way in that they receive information on an RF frequency and inject that information into the APRS-IS. The exception is APRS messages which most I-gates will pass from the Internet to RF. Other position reports, weather data, etc., are not passed from the Internet to RF because it would clog up the local RF networks.
GPS-enabled D-Star stations appear in the APRS-IS through a gateway tool known as DPRS. This gateway is one-way in that D-Star stations may appear in the APRS-IS however other APRS RF users will typically not see the D-Star stations. If I'm mobile and monitoring the local APRS RF network, I will see APRS position reports and information from APRS stations in my area, but I will not see D-Star position reports.
So, the long answer to your question is that D-Star is not a replacement for APRS.