I want to change my transmission from an automatic to a manual

The transmission that fits that truck would be a 2001-2003 NV3500 out of another Dakota. However you will need more than just the transmission as the PCM is different between an automatic and a standard. You will also need to replace both sets of gearing in the axles as they are different as well. The transfer case will need the adapter to bolt it to the manual transmission and you will need to add the clutch pedal and master cylinder to the firewall.
Because of the gearing changes you will also need to flash the body control module so it reads the speed sensors correctly and the security system doesn't lock up due to the different input signal. The easiest way to do this swap would be to find a Dakota that has the same drivetrain and swap over the parts. That way you will have all of the brackets and pieces that you need.

No. Not if you want to keep the 4WD. Even if you eliminate the 4WD you still need to change all the rest of the parts as they are all different from the automatic to a standard. The old days of just swapping parts around are unfortunately gone unless you pretty much build the entire vehicle from the ground up as the computers and controls are integrated into the systems very deep and control multiple items. Even the basic electrical systems are computer controlled in that truck.

Sorry it's not better news but most of the newer stuff makes doing swaps very difficult if you want to keep it somewhat stock and drive it without building a custom vehicle. Even something as simple as replacing just a cylinder head or an engine can be interesting. For instance the 4.7 engine you have in that truck, it was only used in that form in 2002 and 2003, 2004 used an entirely different control system because the company changed to a different design, So even though the newer engine will bolt right into place and all connections are the same, it won't even start because of the changes.
Makes it interesting to do much on the newer vehicles.

No, engine and bell housing patterns are different as are the mounts and shaft splines. Plus the 1998 would lack all of the electronics to interface with the 2003's computer and instruments.

Your 2003 is right in what is almost the worst years for parts interchange that Chrysler ever had. They kept changing things around almost yearly as they tried to make it into a more European company with the result of it becoming a real mess for repairs.