Linux , FAT32 and flash drives

I downloaded Linux Live USB Creator , and it is currently downloading Verve distro with GNOME. There was an option to format my USB drive in FAT32 , which I didn't bother with since the flash drive was already formatted in FAT32 for a BIOS reinstall I recently ran. My question(s) are: Does Linux have to run with the FAT32 format ? One of the options is to run it inside Windows. Would there be any conflict with the MS NTFS file format ? I'm (about to be) brand new to Linux and , like most things , I came up short on knowing where to start learning how to learn it.

Linux has its own file systems (ext 2,3 & 4, xfs, reiser, zfs, btrfs etc etc). It can also understand FAT and NTFS. However, it would ask to format your USB into FAT for the greatest compatibility amongst computers.

During the installation you won't (shouldn't) be installing on a Windows Filesystem. Just not a good idea, even if you could do it, it potentially cause problems

Thanks ! I'm going to install it on the USB drive , so it won't be on the same drive as Winders , much less the same partition. It was indicated I could open Linux without having to boot into it , but I haven't gotten to that point yet.

oh!!!! you're going to like this, I have puppy linux on a 512 mb flash drive.
I can plug it ino any computer and have all my junk right there, pull it out, reboot the machine and noboby even knows it was there, it just loads into memory.
you can access your winders stuff from linux but not the other way around.

I haven't even figured out how to get on line with it yet. The Oracle VM it runs in claims to be tied in to the wireless network , but I seem to be short a browser. And everything else. LOL All I can find are some basic settings. I jumped in to it like I did XP. At least XP had a start menu I could find. I guess I haven't outgrown my propensity to start playing with things and taking them apart before reading the directions. All I've managed to accomplish is giving it two cores of my CPU and two GB of my RAM. It's actually for the rig my daughter is getting. She built her first computer on a coffee table (minus a case) without a mobo manual. She was in the BIOS on the second try. Her only mistake was plugging the monitor in to the integrated graphics and not the discrete card. She was still in the BIOS learning the settings 50 minutes after she pulled the parts out of the box. I was hoping learning Linux would slow her down some. I can see her being well beyond my pathetic skill level after a month of working at it. I'm looking at getting her able to set up a dual boot with Win 10 and Linux and a VM in Winders with a Linux distro.
For a case she wants to build a mineral oil aquarium , because they "look cool". My 15 year old couldn't operate a smart phone a year ago. She discovered her brain and I think I'm in trouble now......

get ready, once a child starts thinking, if that is not killed by saying "do it this way", "it's done like this", they will have you looking like an idiot real quick.

I tried. When it failed to post first time I was about to smugly (but kindly) point out her monitor hook up error. Before I could she said "Oh. Do I have to plug this in here ?" as she pointed out the mismatch. Too late. Independent thought has begun. I don't even know if Winders can stem the tide now.