You can do both of these on the SPARTA GitHub page; see details below.
You can also do this via the SPARTA mail list, by simply sending an email to "sparta-users at lists.sourceforge.net". This would be more appropriate if you are not sure something is a bug, or you just want to know if some feature is already available in SPARTA or possible for you or someone else to implement. If it indeed seems to be a bug, you may get asked to submit the full info through the GitHub site.
Report a bug via GitHub:
If you fix a bug, or implement a new feature, you can submit it via the GitHub site, as a pull request.
Here is the page of currently open pull requests. Click on the checked "Closed" heading to see previous pull requests. Click on "New pull request" to submit a new one.
Document an issue or suggest a new feature via GitHub:
You can browse the details and discussions on previously posted issues, or click the "new issue" button at the top right.
Note that you can add labels to issues. The bug reports are simply issues flagged with a "bug" label.
Regarding bugs, the following quote seems apropos:
As we know, there are known knowns. There are things we know we know. We also know there are known unknowns. That is to say, we know there are some things we do not know. But there are also unknown unknowns, the ones we don't know. -- Donald Rumsfeld
This page lists unknown bugs in SPARTA.