1999 Isuzu Rodeo difficulty climbing uphill

First check the transmission fluid level to make sure it has enough fluid in it (I'm assuming you have a automatic transmission). Next have the vehicle's computer scanned for fault code to know where to start with the "check transmission" light.
Speedometer
This may be related to the transmission issue. The speedometer is controlled all electronically so the issue that would cause the speedometer no to work would be the vehicle speed sensor is faulty, the electrical connectors are no completing the circuit, the wiring in between the vehicle speed sensor and the instrument cluster or the instrument cluster itself.
The fuel gauge is also controlled electronically so the most likely issue is the fuel level sensor is faulty, the electrical connectors not connecting the wiring in between the fuel level sensor and instrument cluster or the cluster itself.
Get the vehicle computer scanned for the check transmission and get back to me, TY