Pay 79p a month for 50Gb cloud storage with Apple, then there is a setting which will make your phone use that to free up storage (and maintain it) on your phone.
It can be a bit of a pain when browsing photos and you don’t have a local copy though.
I think the way to recalibrate your phones battery is to run it down to below 10% and then leave it on an uninterrupted charge to 100%
If you think your battery is totally gone then you can replace it yourself for ~£20, I recently did this on my 5S. I bought the iFixit battery and took set and followed the guide:
https://www.ifixit.com/Guide/iPhone+5s+Battery+Replacement/19239
It’s easy enough, most difficult bit is removing the glue which holds the battery in place. The tooth floss technique sorted me out for 1 tab of glue. I guess the connectors can be a bit fiddly if you’re not used to them. Also be careful removing the old battery, if you damage it they do go bang quite spectacularly.