faith

So the reason for keeping the mitzvot is not because of life after death, and if a person does not want to keep the mitzvot, all is well.

What an Olympic leap!
First, just because it can't be proven doesn't mean it's not true. If you believe in tradition, then that's also a consideration.
Second, life after death is very plausible to me, even if you're not convinced about the afterlife.
Third, the reason for keeping the commandments is not the afterlife, but the truth and the obligation to obey God.

1 True, but it is rational not to believe it
2 Scientifically, not philosophically, perhaps
3 True, but is a person who does not keep a commandment eternally different from someone who does?

Either you believe or you don't. Philosophy and science are tools.
Depends on whether you accept the eternity of the soul. If a person does not exist forever, he cannot be eternally different.

Is the rabbi sure there is life after death?

No. But I'm not sure about anything, not just that.

What does life after death mean if there is no afterlife?

The persistence of the soul means that there is something immaterial within us (a soul, a neshama) that remains after death.
What happens to it and where is it? I have no idea.