Is there a place where I can see updates made to the site with a timestamp, such as feature additions, bug removals, design changes, etc.?
Most of the changes specific to this site can be found under status-completed tag. There aren't many of those.
The majority of feature changes and bug fixes are network-wide, and so they are listed on the network-wide meta. This community-curated list is pretty thorough, with dates and references. Quote:
2015-12-23: Question timeline (not moderator timeline) got a new design and features, e.g. showing who voted to close or reopen, and more.
2015-12-09: Users with 10k reputation can now use the
deleted:1advanced search operator to search their own deleted posts.
- 2015-11-09: Comments auto-added from review queues now indicate as such.
- 2015-10-23: It is now possible to filter your flag history by type.