Downpipe into gully or groound waste (not sure!)

[bowcreek]

Dear members, there are 2 small issues I'm looking your help for.

1. On some parts, specially on right hand side of 2 steps you can see in the picture of stone path, water gets logged because the slope is towards that side. as you can see there is a public footpath behind the fenced area, this being last house on the row. Can I simply drill a hole through to let water drain out ? Its not particularly lot of water but is bit of a problem right after rain. What would be the best way around this please?
Steps
Public Footpath

2. I don't know what is this small square area called where you can see downpipe from small entrance porch and part of main roof (via a junction box) going into a ground pipe. During reasonably heavy rain I see that surrounding void around pipe gets filled up with water and drains slowly after rain stops. I noticed a lot of muck in there. Is there something like a mesh around ground pipe which over the years have hidden under built of debris etc.? Should I expect to see sort of mesh around pipe (potentially for water from patio to drain into underwater pipes) there when I clean it?
Gully

[seanandruby]

I think you just need to get a good broom and sweep away if not a lot. You could cut a rip along there and fill with gravel as a work around so that the water drains away. I would imagine the wall was blackjacked to stop it holding water. As for the gully it looks like ut has silted up and you need to clean it out. Does the 'shoe ' pull off to get your hand in? You may have to cut it if not so that you can get your hand in and pull out the muck, will smell a bit, wear rubber gloves.

[Tony McC]

The ponding on the steps is due to the treads being laid with backfall. You could lift and re-lay the treads to ensure they fall towards the step edge and thereby ensure water cascades down the steps instead of lodging. That would be a more effective fix than trying to drill through a wall.

The mystery gully, if it is a gully, needs cleaning out and checking. A grating will help minimise future clogging.