Indo-European languages are languages that share a common ancestor in Proto-Indo-European, a reconstructed language that we are fairly certain was spoken in the steppes of modern Ukraine and Russian about 6000 years ago, give or take.

Groups migrated out of the steppes and brought their language with them, and that led to a divergence of the migrating groups and the speakers who stayed behind.

You mention that there's 'no connection' between Persian and German, but that's not true. Take a look at this chart, which is not the most helpfully organized, but you can at least ctrl+f "Pers" and you'll see the Persian reflexes of old PIE numerals highlighted. Not all of them are going to be transparently related to the reconstructed forms or to each other, but you can be certain that the forms are related by regular sound change.

Do let me know if you have any more specific questions.