I wonder, are there any guarantees (especially in Europe) that if the plane landed by hour X, I will get my luggage by X+Y? I'd like to buy further train ticket and prefer not to be late, but have as little waiting time as possible.
There is no guarantee or law that provides the assurance you require. This is one of the reasons why many frequent travellers, myself included, travel light and avoid checked luggage so far as is possible.
If your bag is seriously delayed, i.e., it did not arrive on the same plane as you, the airline is responsible for forwarding it to you at your new location. This generally means more than a few hours delay, and often the bag takes a day or so before it arrives.
I know that 30 minutes is enough, but I ask if there are any guarantees, e.g. in a sense of compensation or other laws.
The only legally enforceable guarantee you have is, on an international ticket, that if the bag is not delivered within 21 days, you are entitled to regard it as lost and sue the airline for the value of the contents, up to 1000 special drawing rights. (Which today is about 1300 USD.)
This follows from two provisions of the Montreal Convention on the Unification of Certain Rules for International Carriage by Air, to which many countries are a party, as well as the European Union.
The carrier is liable for damage sustained in case of destruction or loss of, or of damage to, checked baggage upon condition only that
the event which caused the destruction, loss or damage took place on
board the aircraft or during any period within which the checked
baggage was in the charge of the carrier. However, the carrier is not
liable if and to the extent that the damage resulted from the inherent
defect, quality or vice of the baggage. In the case of unchecked
baggage, including personal items, the carrier is liable if the damage
resulted from its fault or that of its servants or agents.
If the carrier admits the loss of the checked baggage, or if the checked baggage has not arrived at the expiration of 21 days after the
date on which it ought to have arrived, the passenger is entitled to
enforce against the carrier the rights which flow from the contract of
The Convention only applies to international tickets, that is, where the ticket includes at least one international sector. Some countries (the UK) also apply its rules on domestic-only tickets.
In my experience, no airline will ever admit this until you actually bring proceedings against them, and then they usually offer to settle the day before the case begins. So it is hardly a consumer-friendly remedy.