Not sure if there is anything you can do about this from the app, but weblink component does not work inside the app. The link is displayed, but the link cannot be opened. I would expect that tapping the link would open it in Safari or Chrome.
It should be opening it in Chrome or Safari, yes. Will re-test this and put it in the next build. Expect to see this fixed by Friday.
This has been fixed in the upcoming version, 1.0.3.
For me, on 1.0.2, i am able to get to home-assistant.io by pressing the logo on the info tab, but there seems to be no way to get back without restarting the app…
Just submitted 1.0.3 to Apple, should be available tomorrow.