Can you select Menu>Settings>Accounts & Sync>Google and then you will see all the Google products that sync. Make sure Picassa Web Albums is selected. If so, then toggle off then on. Make sure you see the Syncing arrows.
The phone may ask you to "Allow" Picassa access to your account. Make sure to select Allow.
Try that out and let us know.
Here is a link as well for general syncing.
That is weird for that to happen. There are a few things you can do.
1. Try to add another Gmail account and test if you can load to picassa. You don't have to set everything up, just another test account. I have 2 gmail accounts, so this may be possible for you.
2. I have preferred to use Picassa Tool from the Play Store. This is a 3rd party app that T-Mobile does not support, but I have found it very useful to use on a personal basis. Link
3. Ensure that all other camera or picture applications are not active or stopping the upload. You can even remove them if need be.
4. This is the most drastic, but a Master Reset. Again, you can make use of other tools instead of this, but if you really prefer to use stock Picassa uploader, then a Master Reset since it is software
Try these steps out and let me know what happens.