Russia does send military jets regularly into other countries airspace. It happens regularly over Iceland for example[0]. The lie is not in saying it happens, the lie is by omission by selectively reporting it when convenient to make it seem that it's something new or surprising. We always see these stories during periods of increased tensions, suggesting that these flights are a response to recent events, when in fact they have been a standard thing for decades. The other omission is that NATO countries (yes, I know Sweden is not in NATO, I'm talking generally here) do the same for the Russians, and western media never reports on that.
I mean, it's understandable, right? The military has to be prepared for lots of different situations, and in order to properly prepare you need to know your neighbors defenses. Finding out at what point your jets get intercepted tells you a lot about what you can get away with. It would practically be negligent of them not to do it.
As for the submarine issue, I'm not familiar enough with it, but I believe you are right that there are no confirmed cases in recent history. That said, I wouldn't be surprised if it's common for Russia and NATO to send subs to probe each others defenses for similar reasons.
[0] http://icelandreview.com/news/2016/09/26/russian-bombers-fly...