Q1: How does one SNAKE a kitchen sink?
Q2: Do you suggest larger-diameter plastic "J" pipes (with a trap door?)?
Q3: What TOOL spins off a 1.5" diameter nipple when only 1/4" sticks out?
Q4: Can a compression fitting attach to the corroded 1/4" steel nipple?

Sorry to not have a picture as I had just returned from celebrating
Easter when my sister called me saying her kitchen sink had suddenly
overflowed during cleanup - so I rushed back to snake it but without my
camera.

Turns out you can't snake a kitchen sink (at least I don't know how)
because one side has a garbage disposal while the other side has a built-
in "cage" of some sort (which I guess comes apart from underneath).

So, instead of snaking it, I looked for that little trap door on the
bottom of the trap curve, but the pipes are all plastic which had no trap
door. So I simply unscrewed the J pipe under the sink, only to find 4
inches thick ground up eggshells blocking the water flow. No problem, I
thought - but then the real problems showed up when I tried to put it all
back together.

The horizontal plastic pipe AFTER the J pipe is supposed to be screwed
onto a 1960's vintage steel threaded 1.5" pipe that juts out of the wall
only about 1/4".

Turns out that steel horizontal pipe is badly corroded. The plastic pipe
after the "J" which fits onto the horizontal pipe has female threads, but
the male threads on the steel pipe are gone - so it's only a press fit
right now. I see a lot of caulking around it - so I'm assuming it was
this way for a while but now it leaks (I didn't have any caulking with me
and all the stores were closed today).

So, what I'd like to ask is advice. Again, I apologize for the lack of
pictures. I'll snap some tomorrow as I told my sis I'd fix it for her in
the morning.

My plan?

I have no idea, but, I might first need to cut a five inch (or so) hole
in the back of the kitchen cabinet plywood with a 4" angle grinder just
to SEE what's there so I can get ideas for the repair.

If I see a 1.5" diameter "nipple", I might try to unscrew it - but - I
can't imagine what TOOL will unscrew a nipple because there is no room to
get a pipe wrench on it since it sticks out so little from the back
cabinet wall.

If I can't unscrew the nipple, then I will try to put some kind of
compression fitting on it (I guess).

Also, I might look for a "J" trap replacement that has an actual TRAP in
it so that we don't have to disassemble it again the next time my sister
puts a few dozen egg's worth of eggshells in the disposal unit.

My questions?
Q1: How does one SNAKE a kitchen sink?
Q2: Do you suggest larger-diameter plastic "J" pipes (with a trap door?)?
Q3: What TOOL spins off a 1.5" diameter nipple when only 1/4" sticks out?
Q4: Can a compression fitting attach to the corroded 1/4" steel nipple?