When you say 'Taking over' do you mean there is something other than grass growing there? If the darker green is simply grass it is probably a bit more nitrogen in some areas. That can be because of a fungus growing there (Like 'Fairy rings'), or some other cause. If you have a few bare patches as well look out for a mixture of grass seed and fertiliser in a box with a pull off strip down the side which reveals five or six holes so you can shake it over the entire lawn, it can fill in the bare spots and green everything up a bit more.
I am not expert, but that looks to me as though the stalks are simply down to the type of fairly coarse grass. When my job folded years ago I bought a mower and made a living for a while cutting lawns and my experience was that the more it is mown the better it gets. There were people who laid lawns with special fine grasses, but mostly the grass that suited the ground took over. If you really want to keep it velvet perfect it needs careful preparation and sowing and a cylinder mower, which I didn't have. To be honest, I don't know for sure about over seeding, but I reckon it won't do any harm, a wire rake would lift some of those coarse stems and give other grasses more of a chance.
We all began at some point, and as you go on you realise that there will always be some aspect where you are still one; that and the fact that when you are dealing with living things things change all the time. Mistrust advice from people who say 'Always' or 'Never'
Welcome to the forum, do you have any other bits of garden, like out the front? Footballs can be pretty destructive to flower beds, as can small boys retrieving them. I have a friend who has a tiny back garden, maybe nine or ten feet each way. His two boys turned it into a mud bath with a ball; he put a narrow raised bed down one side and astro-turf on the remainder, it actually looks pretty good. People have different ideas about what to do with gardens, look about and decide what you want, and when it gets to buying plants remember plants are not like most things, the more they cost the better they are; not with plants. The easier it is to propagate and usually to grow, so the less the nurseryman will charge less. That does not mean it is less attractive necessarily, so look at the cheaper plants.
Just thought, sexist of me, my daughter was in the primary school football team about twenty years ago