You cannot install/update VS without admin rights. There is no workaround for that. It has been requested for years but given it has to install COM components, set shared registry values, etc this is highly unlikely to happen anytime soon. Updates need to have access to the same thing.
Can VS auto-update? Yes it can now. With the latest update you can have VS auto update when you close it. You can read about it here. But you still need admin privileges to do so and therefore after VS closes and the installer starts to run you'll have to agree to the consent screen.
VS extensions, for the most part, do not require admin privileges to install. Any user of VS can install and update extensions because they are per-user. There are some extensions that do require admin privileges either because they use MSI and require admin privileges or simply because of what change they need to make. In this case admin privileges would be needed but these are becoming more rare.