On the File Manager, right-click an SPC file, select "Open with", then "Choose another app". You'll be prompted to choose an application and the option of using it by default when opening SPCs. Choose SPC700, check the option and confirm. Next time you use AMKGUI, it should autoplay the SPC correctly.

YY-CHR doesn't keep your palette settings between instances. Each time you open the program, you'll have to load the SMW .pal file anew. After that, select row 8 to get to Mario's palette, as you've done earlier.

I've taken a look, and it seems you're talking about the last image of this submission specifically. Since it's the only one I could find, I'll be using it as an example.

First, when recording GIFs, make sure that the image is at the proper ratio and no other filters have been applied. This is so the image is clear and doesn't contain unnecessary colors. Your GIF is very blurry due to the anti-aliasing caused by not following this correctly, bumping up the number of colors and consequently the size.

Secondly, if size problems persist, you may need to record shorter GIFs. In this case, your GIF spends plenty of frames wandering around the same spot multiple times. Cutting off frames can help immensely on size reduction.

After that, you can use compression tools like the aforementioned ezgif to automate the rest. Most of these tools also allow for lossy compression should size still be a problem.

To demonstrate, I've made a quick edit of your GIF. Just from applying the second suggestion and some automated compression, the size dropped from 980 KB to just 668 KB.