Email vancewarren57@gmail.com and you will get a reply from the person who wrote the app.
That is deliberate. iOS hands an app the last location it happens to have cached, which can be minutes old and from somewhere else entirely. The app throws that away and waits for a genuinely fresh fix, so your run starts from where you actually are. It should catch up within about ten seconds of open sky.
Because it would not be worth reading. A finish time extrapolated from 200 metres swings wildly. The app shows you how far is left until it has enough to say something honest, then starts.
GPS measures the line you ran; a course is measured along the shortest legal route, and you did not run that. A few seconds either way is normal and expected. The app captures its time at exactly 5.00 km by its own reckoning.
Turn on Settings → Show GPS detail. That puts a line of raw numbers under the run screen: the accuracy of the last fix, how many readings were counted versus held back, and the size of the last step. Send a screenshot of that mid-run and it becomes a solvable problem rather than a guess.
Yes. The phone measures the run on its own. The watch app is an alternative, not a requirement, and shows the same screen.
Not at the moment. The app does one distance deliberately.