The left hand switch is a two-way. Landing light, I guess.
The next switch along is a one way. Porch light, I guess.
These two switches have their commons linked to the third switch from the left, which is in turn connected to the black conductor.
For the lights connected to the two switches on the LHS of the plate to work, that black has to be a live feed, no?
I find it odd that there are plenty of connectors in the switch box. Could one of these contain the disconnected switch wire for the hall light?
And the two reds connected in the back box also intrigue me.
You will deffo need a multimeter at least to try and sort this out.
Edited for clarity.