It sounds like your 50-30 adapter is not working correct.
A 50 amp RV like yours has TWO 120 volt legs feeding it....each at 50 amps a piece (100 amps total). This is called your L1 and L2 legs/lines.
When using an adapter to plug into a 30 amp outlet. then you only have a L1 line, at 30 amps total. This single L1 line has to provide power to your 50 amp RV's L1 and L2 sides. The way the adapter works is that it jumps (shares) the L1 over onto the L2 inside the adapter, so that everything is powered in your RV, but just from the L1 leg/line that is available at the 30 amp outlet.
According to your power cord lights and symptoms, it appears that the adapter is not jumping the L1 over onto the L2 internally, so you only have half (the L1) the stuff getting power.....and the L2 is not getting power.
Try your friends adapter and see if that fixes it. If so, then you know what the problem is, and to get another adapter.
Also remember that even though when using the adapter for your 50 amp RV, that everything is powered, you are now limited in total amps. You went from 100 amps down to 30 amps. You will NOT be able to use everything in your RV at the same time, like you did when you were connected to a 50 amp outlet. Usually this means only one air conditioner can be turned on. and it's best to use your water heater on propane only if applicable. Since your power capability has decreased by over two/thirds, you have to adjust your power usage.
These schematics may help you understand the adapter (with it's internal jumper wire from L1 to L2) and how it powers both legs/lines from a single 30 amp L1. On the first schematic it shows how a 30 amp and then 50 amp outlet are powered. The last one on the far right, is the adapter you are using, with it's internal jumper from the L1 to the L2.
The second schematic shows how your 50 amp RV has TWO 50 amp legs feeding it, and why you are only getting power to one line/leg..
The third schematic shows how a 50 amp and 30 amp outlet are provided power from an electrical service.