I don’t want to join Google+. Can I just keep updating my Picasa Web Albums or will I be forced to transfer them all to Google+? And if the latter, how do I do the transfer?
Whether Google will kill Picasa Web Albums completely for those who don't want to sign up for Google+ is unclear. It certainly looks like that's the way they're going, but I haven't seen any official announcements. I think it may depend in large part on the fate of the Picasa desktop app.
You shouldn't need to do anything to get your photos in Google+. All of my Picasa Web photos were added to my Google+ photos without me having to do anything. (And, actually, all of the photos I had in Google+ were available in Picasa Web Albums.) They have remained in sync ever since.
Even if you join Google+, you still only have one collection of photos which you can still access and manage via either tool, that is Google+ Photos or Picasa-web-albums (PWA). The only exception is photos uploaded via Google Plus pages (ie not personal profiles) which apparently cannot be accessed via PWA (I've been told this, but not yet verified it myself).
There are a large number of people who use Blogger and who have not signed up for Google+. If they have photos in their blogs, then these photos are (be default) stored in PWA. Forcing them all onto Google+ is unlikely, because there will be all sorts of issues with people (like me) who have multiple accounts: I already have a Google+ profile, so am not allowed to set up another one. I've quite deliberately have separated out my accounts so I can have different persona, and potentially give some of them to someone else when I move on from certain volunteer roles (eg the blogs I've built for my choir or for a local mother-and-baby group).
My best guess is that isn't a problem which be solved anytime soon, so I don't expect PWA (at least) to go away.