How can Windows affect Linux & Vice Versa?
 

The title I put is indeed pretty vague sorry for that I just don't know what else to put.

Anyways, to clarify, if I have two seperate partitions on the same hard drive (one for linux and one for Windows) if I am using Windows, could the virus format the partition the windows is on and/or the partition that Ubuntu is on? That is really my main question, im also pretty sure a Windows virus can't "infect" or spread the virus to linux due to permissions/file systems (NTFS and ext4) and the fact that the OS would need to be running to executr anything but maybe it can format or delete the partition. However is it also possible that a virus in linux could format the Windows partition. I don't think linux could spread or infect Windows with the virus because of how it's not capable of running Windows API or .exe's, similar to how I posted above it would require the OS to be running.

I would really appreciate it if you give me feedback in order of the questions that I asked as it will confuse me a lot less. Thanks guys!

Your question about Windows infecting Linux really has two parts:
1. Is it theoretically possible?
2. Has it every happened?
I'll leave part 1 to someone more knowledgeable in partition-theory than me. I have certainly never heard of it happening.
I think the act of using Linux will prompt many people to wipe out their Windows partition and run a Linux-only box. If not sure if that's your worry. :)
jdk

I'm really just worrying about a Windows virus (as its more prominent) formatting a partition/entire hard drive (a partition that Ubuntu is on). (off topic) Funny about how you stated running a linux only box and how people say there aren't enough programs for linux to do so, I just found an amazing distro called ArtistX and it has so many amazing programs (mostly 3d modeling programs but also a lot of audio and video editing) that aren't even on the Ubuntu Software Center I believe and I have never even heard of them. Anyways, back to the topic please.

Yes, a virus or root kit, either of Windows or Linux origin, though the latter is uncommon, could infect or destroy the MBR on your boot disk, or destroy the partition table.

Formatting and deleting partitions in Linux would first require getting root privileges so the root password would need to be accessed. I don't really see why anyone would want to do that as the major purposes of hacking computers is to gain access to data or using it as a bot to access other computers. Obviously, if a computers drives are formatted or partitions are deleted there will be no OS or data. On the other hand, someone who just wants to be nasty and has the skills probably could do it.

Yeah I mean I would say its a bit harder to make a program to look for specific files (well who am I to say) but I would agree if people wanted to be nasty the best way to do it is just to format a hard drive. What do the most common viruses do also? The only one I encountered was that there was a fake program pretending to be like Windows Defender that would show up on Startup, saying my computer had viruses and I needed to purchase the program to remove them (asking for personal info and credit card etc).