2004 VW Jetta 2.0L Automatic Transmission P0734 and P0546 Codes: Causes, Fixes & How to Diagnose Using Factory Manual

Hi everyone, I recently purchased a 2004 MK4 Volkswagen Jetta 2.0L automatic transmission from a tow yard. The car drove smoothly during the drive home and so far, my only maintenance actions were replacing the alternator fuse (which was broken), installing a battery specifically for this model, and changing the oil. I know very little about the car’s history beyond it having a salvaged title — which indicates it was involved in a front-end collision. However, repairs were done professionally, so there's no visible sign of damage when driving or looking at the vehicle. The CarFax shows good maintenance records, and the car has nearly 174,000 miles on it. Since I brought it home, the check engine light has been on continuously. My uncle and I used an OBD2 scanner to pull diagnostic trouble codes (DTCs), which came up as: - P0734: Gear 4 ratio incorrect - P0546: Gas temperature sensor circuit high (Bank 1, Sensor 1) My questions are: 1. Are these two codes related? If yes, how? 2. Could the P0734 code be caused by a faulty speed sensor or another transmission issue? I’ve read several online posts about P0734 — many say that shifting into 4th gear is impossible or that there’s noticeable slipping. But in my car, everything feels normal: power delivery, shifts, acceleration, and no overheating. For the P0546 code, I bought a new gas temperature sensor, but I can’t seem to remove the old one — it's stuck. Can anyone give me step-by-step tips on how to safely remove it? I have the Bentley factory manual (PDF) for my car, and some forums suggest referring to it for P0734 diagnosis. How do I use that manual effectively? I’m new to German cars and manuals in general — I’ve only owned Hondas and a 1994 Mustang GT before. Please explain any advice in simple terms: where things are located, what parts to check, whether I need to replace solenoids or other components, and how to do it step-by-step. No jargon! Thanks in advance for your help! If photos are needed, I’m happy to take them — just let me know how to share them via email or messaging.