Can LISTSERV tell me if my mails are being received and opened? (In other words, can LISTSERV do so-called "open-rate" tracking?)

LISTSERV does not do open rate tracking itself. However, since it acts as a direct pass-through of whatever you post to a list, it does not interfere with any open-rate tracking code (usually HTML that executes when the message is opened) that you might acquire elsewhere and post to a list for this purpose.

If you are looking for a product that integrates seamlessly with LISTSERV to do open-rate tracking (or handle other e-mail marketing chores), you might find L-Soft's LISTSERV Maestro package of interest.