Hi,
Yes I believe they are important, if the page title is too long, Google will typically truncate the title to fit within the guidelines (Around 50-60 Characters).
If this happens, then you run the risk of losing out on important keywords, or having a page title that doesn't really make sense.
If the page title is too short then you'll be losing out on valuable space where you can include important keywords or your brand name!
Page titles in my opinion will always look better, and entice CTR if they follow a similar fashion to my example below:
Keyword | Brand Name
However, I would say don't be too strict on the page title length, for example if you have one that is 48 Characters or 65 Characters long, I wouldn't worry. It's the page titles that are 20 Characters long, you're under utilizing or 90 Characters long that won't be displayed correctly.
I'm not sure what you mean, if Google index keywords beyond 60 Characters, Google will index pages, and the content within it. Page titles are generally used for the link you click within your search results. Hence why they are so important as they should do everything possible to encourage CTR.
Thinks of the page title as the first thing a user will see/notice when looking through the results page.
Hope this helps!
Ian
