Picasa Web is still available (and is a separate product from Google) and Google has just combined Picasa Web into (just for image hosting purpose) Google+.
The help article on Google answers all your questions
If you have Google+ then all photos uploaded from G+ will be resized to 2048px and won't count towards your free storage. But if you upload photos larger than 2048px*2048px from Picasa Web https://picasaweb.google.com/ (if redirected to G+, click on the link in the yellow message box) it won't be resized and will count towards your free storage and when you run out of the free storage, any new images you upload either from G+ or Picasa Web will be resized to 2048px
Read the article for more information.
I won't say that the storage is truly unlimited, if you are a normal user with a normal need for uploading images then it's a kind of unlimited storage. Google will do all it can to provide you as much storage you want to store images but they have some limits too.