Maarten D. de Jong
... please mention which source of rules are you referring to.
Translator of the Dutch rules; long discussions with Wolfgang Kramer.
1) If one side of an empty city space has already been reached by a tunnel, then from the other side of the city space can be started a new tunnel that doesn't need to be connected to anything else: is this correct, or you must build your own station in the city space before starting the new tunnel?
Apply basic building rule: you must extend at least one tunnel. Is that extension occurring solely over a city space? Then you must have a station of your own there; otherwise there is no such requirement.
Example 1: T - T - C - ... - ... (T = tunnel tile, C = city space, ... = empty space)
If you want to place a tunnel tile in the empty space to the right of the city, then you must place a station of your own there.
Example 2: T - T - C - ... - T2
If the tunnel tile you want to place extends both out of the city and of T2, then the basic building rule is already adhered to by the position of T2. You don't need a station on C, therefore. If the tunnel tile doesn't extend out of T2, then the station is required once again.
2) After the explosion of a dynamite tile, I have a station in a city space that isn't reached by any tunnel: can I start a new tunnel from that city space, if this new tunnel isn't connected to anything else?
You can. The city space has two permanent tunnels leading out to the neighbouring spaces. You are extending a tunnel from out of a city solely, and there is a station of your own on the city, so it's allowed.
3) Does an empty city space interrupt the pathway that must be estabilished to build a station on another city space or to prospect?
It interrupts a pathway. See the example on page 5 of the rules, with the Yellow player in particular. This restriction unfortunately hasn't been mentioned explicitly in any version of the rules.