Embedding should work fine as long as you give it a nice clean Twitter link to the tweet:

I would probably do the coastline differently. That blue color doesn't look right when it ends up on the top of the cliffs like that. Maybe a different color, or maybe simply drop it completely. If you keep the "cliff mountains" on the same sheet as the landmass, you could use a glow effect for the coastline that would then trace the actual outside of the combined shape. Another option is to draw the coastline manually as a separate entity, and either skip it at the cliffs, or draw it at their base.

The reason you can't simply change the fill is because they are symbols. Changing the properties of a symbol won't change the entities it is made up from. (May feel weird for a simple symbol like this that is just a single entity, but symbols are often made up of many different entities with different purposes, so just changing them all doesn't make sense). Symbols needs to be exploded before you can change the properties.

This happens because the background is a fill without scaling configured. This means it will repeat to fill the area depending on the resolution, so a high-resolution export will have many more pixels than on-screen display, thereby causing to repeat more.

To fix it, you'll need to click the fill style indicator in the top right, go to the bitmap files tab, find the relevant fill in the dropdown, and then check the "Scaled" option for the fill, and provide proper values for the X/Y size of the scaling. You'll need to experiment with those values to find the correct setting, but once you've found something that works on screen, since it now is scaled, it should then be the same size on exports.

That's just how copyrights works unfortunately. It's still their material to do what they want with even if the products isn't available anymore.

Even if WOTC doesn't keep the patches on their site any more, they're still available using archive.org though. I just tested the links, and they work fine.