So, you say you live in a place with shared network.... Hence I suggest you to use VPN to connect to network whenever needed.
If I disable the network on my laptop, is that enough to be fully sure that no one is able to gather information from my laptop?
Temporarily disabling your network adapters (disabling wifi, disconnecting ethernet cable, etc) wont help you in case of infections. Trojans can gather the info and wait in background till you are connected to internet, to call their home. So, the first defense in place must be safe browsing and a good set of security software and tools.
Now suppose you are disconnected from network for the entire life of PC, but if you connect an infected USB any external device, it can infect your PC and if enough sophosticated, the can use these devices to upload the data to their servers via another PC.. Not to mention, your softwares will not be uptodate nor patched.
If I use a USB-stick to transfer files from a PC(with internet access) to my laptop(no internet access), then put some wordpad text files from my laptop on the USB stick, then insert this usb stick back into the PC (with a trojan). Will the PC only have access to the wordpad text files I put on the USB stick, or will it automatically have access to all the other wordpad files on my laptop (which I did not put on the USB)?
See above as well as:
No, the PC will have access only to your files on USB stick. But, the trojan may have infected your 'Air gapped' PC by this data tranfer. So it all can depend on the infection also.
Can the laptop somehow automatically go nuts and connect to the internet in the future by itself? (Like cause I havent' activated my windows or w/e).
No, Not heard of any infection doing such a weird activity. Malicious software needs to be too sophosticated to do so... Currently very rare in PoC (Proof of Concept) also. But in field of malware and threats, nothing is future proof!
If I write something down today, but connect to the internet next week. Will a super spyware or trojan or whatever, be able to gather data of things I wrote today?
If you got infected somehow, then yes. Well, malwares like keyloggers may be. If the attacker can grab a screen shot in the 'next week' unfortunately while you opened what you wrote today, at that time of infection.
May be, if the malware can search through the readable files (like text, documents, pdfs etc and you used one of such file, then it can transmit the data gathered to server. But this can be an extremely rare possiblity.)
So, you must first prevent incidents so you dont need to worry about it later.
Bottom line: You have to secure your docs and data as much as possible and protect your machine from threats.