If I went to an alien planet that supports life, could I catch alien diseases?
Unlikely, at least in short term.
A potential pathogen needs to evolve with its host. It has to figure out the which organism might be useful for its life cycle, suitable ports of entry and mechanism for fooling defence mechnism of the potential host. And it will have to do it by blind repeated cycles of selection till the potential pathogen has developed all anatomical and biochemical arsenals necessary for invasion and derive benefit out of it.
An alien cannot just crawl upon you for the first time and cause a disease.
It depends literally on the nature of that planet:
Are there living beings based on carbon or a different stuff?
Do they require water?
Do they require oxygen?
I imagine it is quite difficult to catch a disease based on a sulphite life form when youre oxygen-based.
But then again maybe there are sound-transmitted viruses that can implant their physical component by manipulating any sound sensors including your ears, resulting in a corrupted area around your ears that grows into a huge biological microphone that again sends out the soundwaves to reproduce...
Is there a Native American who would like to answer this question.
Very unlikely. There are not that many diseases that make the jump from one species to another compared to those that don't, and this is already between species on the same planet which share many similarities AND it requires a long period of evolution so that the pathogen can evolve to adjust to the new organism.
It boils down to two schools of thought.
One points out that diseases evolve to affect specific plants or animals, even just on a single planet. So the likelihood they could affect a life form that's not even from their planet is essentially non-existent.
The other school points out that microrganisms are tricky, and frequently surprise us even just on this planet...who knows what they might have evolved on a totally different one...
Since we only know about life on just one planet so far...we really don't know.
It's going to vary tremendously with the life forms. For organisms which depend on interacting with host cells and tissues (all viruses, most intracellular parasites, many extracellular pathogens) it would be virtually impossible due to the differences in biochemistry. For "blunt force" organisms that break down anything they come in contact with, it might be possible if they have "digestive enzymes" that will work on our cells. It will also depend on how different their biochemistry is from ours. If extremely different, they may not be able to establish an effective presence if our biomolecules are not anything they can use. So the answer is yes, no, maybe and possibly interactions we cannot even imagine.