If it's just for the currently logged in user, you can use /api/v3/users/me. There's also /api/v3/users/{userId}/get to get the user with any id. Those both exist prior to 3.5, but that probably doesn't matter now that you've upgraded. In 3.5 and onwards, there's also additional APIs to get the user by their username or email as well if necessary.
As for the other changes to the API, we made some changes in 3.5 to help performance on the webapp, but we should've paid more attention to backwards compatibility for integration developers. Going forward, we're hoping to give significant warning of any APIs that will be changed or removed (at least a few months) to keep this from happening again