First of all, fair warning I’m not the best artist and have little experience to speak of. With that out of the way I’ll answer a few of your questions.
First off for making gifs of your work you will need a program to help you do so.
This thread here was pretty helpful to me
http://wayofthepixel.net/pixelation/index.php?topic=3467.0I personally use gimp for all my pixel needs.
In regards to your color pallet, its something I struggle with as well but ill do my best. What you are looking for is contrast within your colors so that they define features.
Because since sprite art is really small detailing becomes quite difficult. It helps to have a light source in mind; I arbitrarily picked a light source coming from the top left.
He was in kind of in strange pose which makes him look uncomfortable. I widened his stance a bit and made him a bit taller with the addition of small shoes. I apologize if that’s not what you were going for I’m not used to working at with smaller sprites.
As for the animation the swing is missing a few key things, the anticipation frames and the follow through or recovery frames. It’s much better explained in the animators survival guide by Richard Williams which I think is a must read for anyone animating.
I’ll try to vaguely explain it as best I can. Anticipation basically is the movement that happens before the “main movement”. In this case when you swing a sword you rotate back a little before you swing kind of like gathering energy for the action. A better example is to throw a punch you have to pull your arm back.
Follow-through or recovery is the frame after the contact frame. Like following through a fold swing after you hit the ball you don’t just hit the ball and stop your swing there.
So with that in mind I did a rough edit of the sword animation. Here is a comparison, i didn't know your timings for the frames so i just did 100ms. I also don't know your original character design but in my head a samurai would only swing this way if he had a sheath, so i gave him one.
Hopefully this helps.