Written plainly, because a privacy page you need a lawyer for isn't one.
Everything. Text recognition, classification, field extraction and search all use Apple's on-device frameworks — the Vision framework and Foundation Models on the Neural Engine. There is no Nilad server. There couldn't be a data breach of your documents at our end, because nothing of yours is at our end.
Your library is a single package on your Mac containing the original files and what Nilad read from them. It doesn't sync anywhere. If optional iCloud syncing arrives in a future version, it will go through your own iCloud account under Apple's terms — never a Nilad server, because there isn't one.
Nothing, from the app itself. Purchases and subscriptions go through the App Store — that's between your Apple account and Apple. The app has no analytics, no crash reporter that phones home, no accounts and no email list. The app's Settings include a network log; the honest expectation is that it stays empty.
Static pages, no cookies, no trackers, self-hosted fonts.
Settings → Library → Export everything. You get every document as a searchable PDF plus a CSV of everything Nilad read, whether or not you're paying. Then delete the app. Done.
Nilad is an app you buy, not a service you feed — your documents are read by your Mac, stay on your Mac, and can walk out the door with you any time.