I'd like to know if sneaking into abandoned buildings for fun is haram? Also the ruling on sneaking into buildings to use their paid services (e.g. gym).
Although it's not exactly the same as entering an abandoned building, there's a Qur'an verse which describes how one should enter another's house:
O you who have believed, do not enter houses other than your own houses until you ascertain welcome and greet their inhabitants. That is best for you; perhaps you will be reminded.
Here we need permission to enter (which is unsurprising, really). There's also a hadith which applies to entering without permission:
The order of taking permission to enter has been enjoined because of that sight, (that one should not look unlawfully at the state of others).
Sahih al-Bukhari 6241
So sneaking into houses is forbidden, and there seems no reason to believe Allah would have a different stance towards other property.
Moreover, sneaking into buildings would be considered trespassing, and is probably illegal. Muslims are required to obey the law of the land (Darul Iftaa). There may also be matters such as safety to take into account: i.e., there might be guard dogs, or maybe some of the structures may collapse.
Sneaking into buildings to use their paid services would be considered theft of services and is probably just as illegal as theft of goods. Another form of using services without paying is considered haram:
It is not permissible to use public transportation without paying the fees if there are tickets for it.