Regarding the corrosion… you can see the assembly instructions for the hot-end here: https://ohai.lulzbot.com/project/cf3b0638-1e1e-4bff-a00e-c3308d914c68/hot-end-tool-head-assembly/
Scroll through that page and look at the photos… if it’s that blue stuff you see in those photos, that’s normal and not corrosion.
But… brass is soft and those extruder nozzles do wear over time and occasionally have to be swapped for a fresh nozzle (a replacement nozzle is about $10).
You may want to clean up your heater block. You wont get it to look shiny new… but you should be able to get all the obvious clumps of filament build-up off.
You can clean up the heater block by just getting it hot (hot enough to melt the filament). I use tweezers to pull away any good. You can use a putty knife (careful not to touch any wires … you may wan’t to get it “hot” and then switch off the power so you can clean near the wires without a risk of shock and blowing a fuse) as it gently cools down. You can also use a scotch-brite pad. (LulzBot supplies red scotch-brite pads for cleaning the nozzles in the accessory toolkit that comes with new printers.)
Regarding it not extruding when actually printing a part… it’s possible the nozzle is too close to the bed.
See this page: https://ohai.lulzbot.com/project/mini-104-calibration/mini-v104/
Particularly, check step 7 … setting the Z-offset. Initially they show how to set it to -0.8. That should be too high … but at that height the nozzle will definitely not be touching the bed so the filament should not be blocked … it should flow easily (although the part will probably look awful because the filament is basically “falling” onto the bed.). They want you to bump the z-offset down another -0.1mm at a time until you get a good nozzle height.
My “guess” is that you’ll find a decent z-offset is probably somewhere in the neighborhood of -1.2.
You can measure it … assuming the filament is flowing, let Cura create a part and lay down a “skirt” around the part to get the filament flowing. Once the skirt is finished, abort the print … pull it off the bed, and grab some calipers and measure the thickness of the skirt at several points all the way around the print. You want to make sure one side isn’t significantly thicker or thiner than the other. And you want to confirm that it’s very close to the first-layer height that you set in Cura (e.g. if you tell it to 0.25mm layer heigh but the first layer height is 0.35mm then you want the readings to be close to 0.35mm with your calipers. Again… measure lots of different spots because you’ll find it will vary.
If you get a lot of variance, your nozzle may not have been clean when it probed for level (or it could mean a washer is a little loose).