To start your plan from the runs you have actually done, to show how today compares with your own normal, and to fill in your profile. Trig only ever reads from Health — it never writes anything to it — and it never sends anything it reads anywhere.
iPhone only asks once. To change it, open the Health app, tap your profile picture, then Apps → Trig, and turn on what you want Trig to read.
To read the temperature and dew point where you run, so your paces can allow for the heat. It is only used while the app is open.
To notice when something might clash with a training session, so it can suggest moving it. Trig never adds, changes or deletes anything on your calendar.
Weather needs an internet connection and Location allowed for Trig (Settings → Privacy & Security → Location Services → Trig).
On your iPhone, and only there — there is no account and no Trig server. To keep a copy, use Settings → Export my training: a spreadsheet of every session that opens in Numbers, Excel or Google Sheets.
The full details are in the privacy policy.