Lawn invader & patchiness

Fitzchiv

 

Hi all, first post on here and it's a couple of questions about my lawn (new turf laid last sept)

The ground was levelled by a contractor digging the foundation for a patio, having previously been a smaller lawn area, overgrown beds and unsafe pond (I have a toddler) and then a local firm with a good reputation added topsoil and turfed. In between the two I worked the ground and removed as many weeds etc as I could feasibly do - with a good 8 week gap for them to grow in the levelled earth and the turfing company coming in. Anyway, long story short I've noticed the turf is failing to thrive in one area - with a "spongy" feeling under foot as though it's being lifted from beneath. Before long some leaves started showing through and although plucked and cut (before winter) they keep on pushing through. So question 1 is - any idea what the plant is and how I can deal with this?! The plant is in the bottom left of the first image in its full glory (below the one I was taking a photo of) but can be seen in the next two pushing through. 

The next is a bit more straight forward, the lawn is thriving along the edges but is noticeably less so in the middle strip and especially around the patio - as per final image. Any idea what may be causing that and how I can help the less abundant areas?

For the next few years this space has to be flat, safe and durable for a little boy to play in - before we start introducing more pots, beds and plants etc for him to then learn about gardening. As you may be able to tell I'm not massively green fingered - my forte is the building sheds and laying flags bit!

Any advice gratefully received!