What is this sticky nonsense, and how do i get rid of it?

Scale insects... - you can try neem oil, but all the online tutorials say to just pluck them off, or dab each one with alchohol. It seems they are nearly impossible to completely get rid of.

Yep, scale.

The brown spots are the insects. They sticky stuff is sap the insects excrete.

Best option:

Take your plant into the shower, and thoroughly rinse the leaves.

Once it's dry, take a toothpick and scrape off as many of the insects as you can see. An old soft toothbrush also works well. Make sure you check the underside of the leaves, and all of the stems.

BUY some 'insecticidal soap' spray. Don't try to make your own. It's totally harmless stuff, so don't be scared by the word "insecticidal". Spray the plant thoroughly, including under the leaves.

Repeat the scraping and spraying once a week or so.

Agree w/ others, and keep it away from other plants. Actually, check your other plants too if you have them. I hate scale >_<

Q tip dipped in hort oil or rubbing alcohol has worked for me in the past - seems to swipe them off easily.

yep. scale. this stuff worked better than anything else i've used. the first time i rubbed every godforsaken leaf with alcohol and it still died. this stuff saved them. also works for those little fungus gnats you get in the soil.