When you import manually from the iPhone using a USB connection to a computer, you will import just the naked original media files, as you have saved them right from the camera or an app, the image files, the videos, the Live Photos, etc., but not the organisation of your photos in albums and folders.
If you want to transfer the Photos Library from the iPhone with its structure and all adjustments you applied, you will have to use iCloud Photos. Only iCloud Photos will give you a perfect syncing. If you enable iCloud Photos on your iPhone and your computer (iCloud Windows on a Windows PC), the Photos Libraries on all your synced devices will automatically be kept identical. Any modification you are applying to your photos on one of your devices will be synced to iCloud and from there it will be synced to your other devices and update the library there. All albums and folders will be the same across all the devices, with the same captions, dates, favorite hearts, places, even the same keywords. You will not see the keywords on the iPhone, but can search for them.
You will need a subscription to iCloud + to keep 80GB of photos in iCloud, however.
Here is how to set up iCloud Photos on your iPhone: Use iCloud Photos on iPhone – Apple Support (UK)
And on your other devices: Apple Support article: Set up and use iCloud Photos
Added: I forgot to answer your question about the deleted photos. The items in the Recently Deleted album will also be downloaded, when you download from the iPhone. Did you empty Recently Deleted, before you started to download your Photos from the iPhone?
