No, I don't think you can bring your own drinks typically in Japan. I've never seen it. I haven't tried though.
However, unlike Europe, water is free and even though it's tap water, it's really good (Tokyo has excellent municipal water quality). European restaurants are terrible that way; they want to sell you ridiculously expensive bottled water that costs more than alcohol.
You can "get by without" tipping in Europe, but in some places (like Budapest) they try to guilt tourists into tipping the same way it's done in America with a place on the credit card slip while the server is watching, because they know American tourists are used to tipping a lot. Other places have a place to add a tip too. Japan is different: there is absolutely no tipping, whatsoever. It's not even allowed; they will return your money to you.