Sources need not be online: regrettably, there are many books, journals, and newspapers which are not yet available on the Internet. (Or they may be online, but behind a paywall.) If the best source is a book from your friendly local library, then by all means use it and cite it. Even if other people can't click the link to see your source, they could still - at least in principle - go to their own libraries.
If the source is "a conversation I had" then this is not possible. While there are standard ways to cite private letters and conversations, that doesn't mean that it's a good idea. It does at least let people know the provenance of your information, but it doesn't do much to help them verify it. Indeed, there are all kinds of things that unscrupulous users could try to pass off, if they're allowed to cite a conversation rather than an accessible source. 1 These kinds of appeal to authority just end up as empty rhetorical devices, if there's no reasonable way to verify them. 2
For this site, there can't be many questions where personal communication is the only source available. Even if you have to talk to an offline expert, they should still be able to point you to a reliable written source. Then you can cite that, and acknowledge the expert.
(I'm not sure what your second paragraph is asking, so I haven't tried to answer it.)
1. N. T. Wright. Personal communication.
2. God. Personal communication.