Yes, sammeln is related to English same, Greek hama, homos, Old Irish som 'the same', samail 'image, picture', Welsh hafal , Breton haval 'similar, like'. From the PIE *sem- 'one' which also gives Latin semper 'always' and German sanft 'soft'. As for the Finnish, your guess is as good as mine. I keep meaning to get a good historical Finnish dictionary.