Your lower case "i" is pretty easy, and you don't really need GREP to do it Just enter i in the plain text find field, and I in the change field, and click the "whole word" button at far right down below. That said, if you want to use GREP, \bi\b should find it, and change to I as before.
Your other probelm is much more complex. First, unless each line is a separate paragraph, Find/Change has no way to find the first character in every line. The next problem is that Find/Change has no ability to do a proper change of case on random characters, though for your purposes it might be sufficient to change the case to All Caps for the first character, which is possible either directly or though the application of a style, but it isn't very elegant.
Finding the first character in the line may be doable via scripting, though, and you should ask in the scripting forum: InDesign Scripting
If you go to preferences
AutoCorrect Capitalisation Errors
Fixes all your problems and no GREP needed
How does autocorrect change the first character of every line to uppercase? In a normal paragraph that would be an error.
Thankyou Peter. I've saved the 'I' automation (both GREP and text versions).
As for the second request, I should have made it clear that I meant each new paragraph in a specified style as opposed to each new line. So it will always follow a paragraph return. Does that simplify the options?
I thought they meant each new paragraph
As it turns out, Eugen, you were right about the intent.
@ spenno, if you don't like Eugene's solution, you can search for ^. which is the first character in a paragraph, then set the Change Format to set the case to All Caps.