You mentioned that popping the disk in didn't "feel right" -- do you mean mechanically?
If so, you probably want to take your SE/30's floppy drive out, clear out all of the old grease, and re-lubricate it. I use WD-40 for both tasks, though a slightly heavier oil like 3-in-1 would be a good choice for re-lubrication. After you've gotten the new lubricant in, find a floppy you don't care about and work it in and out of the mechanism using the manual eject lever, until the drive auto-injects smoothly. There are little rollers along the sides of the drive you need to pay special attention to. Lubricate the spindle bearings too, and give the drive motor a spin with your finger to work the new oil in. After all that, wrap a floppy disk in a paper towel, and insert it wrong-side-first (metal tab end toward you, away from the drive) to pick up any extra oil.
Most of the old Macs I've restored had "failed" auto-inject drives that either wouldn't inject/eject or wouldn't read due to poor lubrication. I've gotten 100% of the working again, with a little care. Often, a drive that injects/ejects alright will have old gummed up grease around the spindle bearings, and that makes the disk spin slow.
Do you have an older Mac with a floppy drive to make disks from? Another 68k capable of booting the OS you want to install, with a known good floppy drive would be ideal. That way you can write out your disk image, and try to boot the machine you wrote it with using the new floppy. If you don't have a way to make floppies from images, PM me and I can send you a System 6 or System 7 disk set from the images.
About the SE/30 video problems: this is often due to a bad capacitor, or capacitors. Apple made a poor choice in one of the SE/30's analog board capacitors, it's an electrolytic when it should be at least a low-ESR electrolytic. If you need a replacement, I've got plenty of high-quality film capacitors of the correct value, which are both easier to install and better-looking than the "pile of ceramic disks" people often use!