HI there Florasmum,
It sounds like you are manually deleting photos but they aren't actually being removed and are still taking space and your recently taken photos aren't showing up in the camera roll. When you delete photos they are moved to a Recently Deleted album that automatically empties after 30 days in case you need one of them again. Luckily you can delete them manually as well:
Delete a photo or video from Photos. Tap the Photos tab, tap the photo or video, tap
, then tap Delete Photo or Delete Video. Deleted photos and videos are kept in the Recently Deleted album on iPhone, with a badge showing the remaining days until the item is permanently removed from iPhone. To delete the photo or video permanently before the days expire, tap the item, tap Delete, then tap Delete Photo or Delete Video. If you use iCloud Photo Library, deleted photos and videos are permanently removed from all your devices using iCloud Photo Library with the same Apple ID.
From: Organize photos and videos
As far as new photos not appearing I would first make sure you've checked in the All Photos album:
View all your photos and videos. By default, Photos displays a representative subset of your photos when you view by year or by collection. To see all your photos and videos, go to Settings > Photos & Camera, then turn off Summarize Photos.
From: View photos and videos
If you have and they aren't there then something may not be indexing correctly so I would quit the Photos and the Settings apps:
Force an app to close in iOS
1. Press the Home button two times quickly. You'll see small previews of your recently used apps.
2. Swipe left to find the app you want to close.
3. Swipe up on the app's preview to close it.
When you have done that restart the device and test the issue again:
iOS: Turning off and on (restarting) and resetting
Thank you for using Apple Support Communities, let us know how that goes so we can provide additional assistance if needed!