Unfortunately not so simple to tell on iOS - TagInfo and other apps can only scan tags with an NDEF data record on them, it won’t give data on any other HF tag or let you format them.
If I had to take guesses based off your photos - hotel card might be cloneable, there are good odds on Mifare Classic (in luck if you get an xM1) and Mifare Ultralight (not as much luck). It could be LF or could be something else HF, its really hard to tell, but its less likely than the two above options.
As for bus pass, probably HF, probably secure and uncloneable, and honestly at this stage it’s not worth it even if you can technically make it work. Meow-Ludo Disco Gamma Meow-Meow set the precedent in Australia - short version is that he got fined and dragged into court because Sydney’s public transport didn’t agree that his ‘tampered’ opal card was still a valid ticket so charged him with fare evasion. He’s paid at least $1k in court costs, but they eventually dropped the fine and charges because fare evasion wasn’t his intent and he still paid for his ticket. To this day, I think they have still disabled his implanted card because of their terms of service. This is a long way to say that Australia isn’t biohacker friendly on Public Transport, nor are most places in the world, so I’d hold off till they are.
Finally, payment! Apex will do the job once a bank jumps on board. Australian banks are very slow on adopting new things (Apple Pay was incredible if you remember the stories in the news) so probably a few years for me on this side of the world, less so in other places.
That said, don’t be discouraged, NExT chips are still a lot of fun, just may not be able to do all you want to at this point in time.
Greetings from Melbourne,
Compgeek