Help! Inherited garden no idea what I am doing.

If you do not have one a hedge trimmer will come in handy. I have just purchased a cheap one and it works just as well as my last expensive one which I threw out as a new battery was more expensive than what I paid for it.

 

In your 2nd pic, it's a buddleia that's sprawled across the site a bit. As already said, that can be pruned back, at almost any time, and people often take it back a bit at this time of year to avoid rocking and dislodging it through rough weather. The main pruning is done in late winter, when you hack it right back, as it flowers on the new growth it makes through the season.
The pink flowered plant beside the stepping stones in your following pic, and in some others, are Japanese anemones, which can be a bit invasive, but that only matters if you don't like them! They don't need much attention, but some may need supports depending on where they're sited.

Those hydrangeas can be pruned back a bit in late winter/early spring. If they're a bit floppy, it can often be due to lush growth by too much food and/or a lot of rain encouraging that growth. A sturdy support put in after pruning will help though.
Always easier to do a couple of plants at a time, with close ups of flowers and foliage, so that you get help with IDs. As @NigelJ says, the addition of your rough location always helps, because there are huge variations in the UK, which many people don't realise.

I'd try and nuke that bamboo too if you can. It can cause a lot of problems. There are better plants, and ones that won't cause future problems.

 

In the same area @fairygirl I think the stems laying on the paving are also Buddleja - one of the yellow varieties. They can both be cut back as you explained.

 

I think you're right @Sheal. A closer pic would help ID for sure, but there does seem to be branches right at the back - in front of the grey wall.
It doesn't look like there's a lot of room for those three shrubs @Leafylearner - 2 buddleias and a hydrangea, and there's other shrubby/woody planting there too, but it may just be the angle of the pic.
The good thing about buddleias is, they're easy to grow from cuttings. The cultivated varieties aren't the same as the wild, common one which seeds around, and I'd expect that one is a cultivated variety. If the space is too tight for them all to be at their best, you could remove the one on the left by constantly cutting it right back to the ankles, and use the material for cuttings to grow on and plant somewhere else if you had a site for it.
You'd get help doing that if you wanted to try it, but they're among the easiest shrubs to propagate.

 

I think the larger Buddleja sprawling on the left was possibly planted to screen the wall behind, but it needs pruning down to about knee height. Don't worry about harsh pruning it @Leafylearner, they grow very quickly and are tough plants. The yellow one I'd be inclined to dig out and plant elsewhere as it's not helping what seems to be two different Hydrangeas planted in front of it. With that gone I think the Hydrangeas will become more upright in time.

 

I couldn't make my mind up about the hydrangea either @Sheal. It looks like a paniculata and a mophead, but I wasn't sure if it was just the pic. Hard to tell.