Okay this is incredibly basic but I can't find an answer on Google. I have notated chord-only sheets in 4/4 that use four slashes per measure. If I'm notating something in 2/4 I use two slashes per measure, is that correct?

Also, does anyone know where I can view an example of a 2/4 chord lead sheet online? Again, I've been searching Google for an hour and can't find anything.

You're right: 2 slashes per measure for 2/4.

I have another notation question, this time regarding accidentals. I couldn't find an answer to this in either of my notation books and a Google search turned up conflicting information to what I remember.

Let's say I'm in the key of F (one flat). I have an F that needs to be a semitone up (F# or Gb). I seem to remember from my limited music training of long ago that if you're in a flat key (F, Bb, Eb, etc.) you always write accidentals as flats. So in this case it would always be notated Gb. Correspondingly, in sharp keys (G, D, A, etc.) accidentals are always sharp. If what I remember is correct, the following two are correct:
D E Gb G-natural A
A G Gb E D

However, I looked at some sample scores and this looks like it's not the case. I did a Google search and what I found was that if the next note following the accidental is a higher pitch you notate the accidental as a sharp, and if it's a lower pitch you notate it as a flat. It doesn't matter what the key signature is. If this is the case, proper notation would be:
D E F# G A
and
A G Gb E D

Which is correct, the way I remember or the way I read about today (or something else entirely)?

Neither is universally correct for the reasons that you state.

It depends on your harmonic intentions. Are you augmenting an F or diminishing a G? Where does the note fit in with the other notes?

For example, is it part of a chord? If you can name the chord as it fits into the key of the piece, the name will tell you what the letter name should be and what's its appropriate accidental would be. Also, the melodic intent might decide the accidental. A minor scale, for example, would always have a diminished third degree, resulting in either a flat (if the note is natural in the key signature), a natural (if the note is sharp in the key signature), or a double-flat (if the note is already flat in the key signature).

In the case that none of these strategies apply, like for a transitional tone, or a purely chromatic passage, I believe the convention is to use accidentals like the key signature (your first proposal).

Don
Kansas City

wing fat, as Don says, there isn't a precise answer.

In melodic movement though, and chromatic movement (F F# G) when you go up you put sharps and when you go down (G Gb F) you put flats. This way you don't have to use the natural sign.

When in melodic movement there are intervals, you try for the ordinary interval (which can be hard some times). I mean if you want to go B to F# you don't put B Gb, but B F#. If though then you want Bb, it's preferable to put B F# A#, and not B F# Bb. I hope it makes sense.

In harmony the same rules applies pretty much. when you have a normal maj, min, normal chords anyways, you try to notate them as normal as possible and in the key that you are.