Is it bad that I still don't really get Kirchhoff's Current Law?

Guessing arrow directions and flipping the sign at the end is not cheating, it is literally the standard method. Nobody, including your professor, knows which way current flows through some random resistor before doing any math. You pick an arrow, write the equation, and if the answer comes out negative it just means the current actually flows the other way. A negative answer is information, not a mistake. The two negative signs in your homework problem probaly happened for one of two reasons. Either the problem statement defined two of the current arrows pointing away from the node when you were summing currents into it, so they picked up a minus sign when you moved them to the other side of the equation. Or you solved it and got negative values, which just means those arrows point opposite to reality. Both are totally normal and both give you the right answer as long as you stay consistent. The trick that made it click for me: before writing anything, I literally write down at the top of the page something like 'currents in equal currents out' and mark each arrow with a plus or minus depending on wether it points in or out of the node. Then it becomes pure bookkeeping. Every current gets one term, in is positive, out is negative (or the reverse, your choice, just pick one and stick with it for that node). If you flip conventions halfway through a problem, that is when errors happen.

As for your lab partner seeming to just know the direction, that is pattern recognition from doing a bunch of these, plus knowing that current through a resistor flows from higher voltage to lower voltage. Once you have solved enough nodes it becomes automatic, but they went through the same guess-and-flip phase you are in now, probably earlier in the semester.

Two weeks is plenty of time. Do ten or fifteen node problems by hand with explicit arrow labels and the sign confusion mostly disappears. The pun is still dumb though, and I mean that affectionately.

What fixed it for me was plugging the answers back into the node after solving. Add up all the currents with the signs you got and see if they cancel to zero. Takes ten seconds and if the check fails you know you flipped a sign somewhere instead of finding out when the midterm comes back graded. I did that on every single homework problem for a few weeks and it built the habit fast. Also stopped losing points on multi-node problems because the check catches the one bad equation before it poisons the rest of the page.

I'd push back on the part where you say nobody can know the current direction before doing any math, because that's only true when the problem gives you no voltage info. If the diagram marks polarities across the resistor, you absolutely can call the direction before writing a single equation, since current runs downhill from high to low. That's probably why the lab partner looks psychic. Where the guess-and-flip method actually earns its keep is when the problem only gives you resistor values and one source, so the direction falls out of the algebra instead.

Update: tried the plugging-back-in check from the second reply and it allready caught a flipped sign on my homework, so that one's staying in the routine. Still stuck on what the last reply said though. If the diagram marks the polarities across a resistor, do I point my arrow to match the marked polarity, or does that not matter as long as I stay consistent? Midterm panic says I should stop guessing this part too.