What is the best way to make the Puck log data and read it by mobile? Any ready code for that?

I want to display my temperature and brightness into my webpage with two input text fields

That should be fine. Just use the code document.getElementById("mytextinput").value = whatever_you_got; for each input field - I'm pretty sure I posted some example code for getting the data from Puck.js on one of the other posts you made?

I tried to use Bootstrap to make my webpage look fancier but the bluetooth connection window doesn't show up.. is there any problem with that?

There shouldn't be - I've seen bootstrap sites use Web Bluetooth before. Have you looked in the developer console to see if there are any errors?

You can't make the connection window appear at startup - it has to be in response to a user's click... so that might be one problem?