Strange light issue, please help troubleshooting

Hi all,
I hope that someone could help out.
This is a 2004 Acura RSX-S. After uninstalling the front bumper, I removed the headlight projectors to test some new LED bulbs that I recently bought. They didn’t do as much light as the halo bulbs, so I discarded them and reinstalled the original halo bulbs.
Both lights, the low and high beam are not working properly on the passenger side, while they are perfectly working on the driver side.
1) First issue is that on the passenger side they are not bright as they should, the light is really low (check picture below). Also, I need to plug both lights into the connector in order for them to turn on. If I plug only one light, they don’t turn on. This problem doesn’t happen on the driver side, where I can plug only one light at time and they turn on.

Picture 1

2) Second issue is that when I turn on the high beams, both low and high beam shut off. Check the picture below. The driver side is fine, while the passenger side lights are off.

Picture 2

I did the following testing:
- I checked all the fuses one by one and they all seem to be fine. Also if a fuse was broken, then the light wouldn’t turn on at all.
- I removed the light bulbs from the passenger side and installed to the driver side and vice versa. Same exact issue. Thus, the light bulbs seem to work perfectly fine. I guess that the issue is somewhere else and I don’t know where.
What could cause this issue? What other components should I check/replace?
Thanks in advance. If you have questions, please let me know and I’ll answer promptly.