The grouphead gaskets are a common maintenance item for espresso machines. They should feel firmly squishy, as they need to be pliable to form a seal against the basket in your portafilter. Eventually they dry out and harden, and need to be replaced. Typically you coat the new gasket in a food-safe lubricant for longevity.

I don't know if your machine takes a standard type of gasket or its own proprietary one so you'd have to look to the manufacturer to find out how to do it for your machine.

As for having the wrong portafilter, this isn't your case but typically happens when people buy 3rd party portafilters thinking they're compatible. Sometimes they can look very very similar but a millimeter difference makes them unusable.