First of all take a look at a resource pack guide like this one https://forums.terraria.org/index.php?threads/the-ultimate-guide-to-content-creation-and-use-for-the-terraria-workshop.100652/

second, your new sprite must be EXACTLY the same dimensions as the one you are replacing or it will not work.

I suggest drawing over the current sprites when you make your new ones so if they're animated, you know they will move how you want them to. If they aren't its still good to have them centred if anything.

To access the current files it should be under: C: > Program Files (x86) > Steam > steamapps > common > Terraria > Content > Images or at least that's there they are for me. You may need to get something that unpacks .xnb files to see the .png files. don't worry, you don't need anything to repack them because .png files work in your mods folder.

For the pets that follow you they are labelled as a "projectile" You can just look up what the id is on the terraria wiki. Just go to the page for your favourite pet and look at the id. For example the fennec fox on the wiki says "Internal Projectile ID: 816" so the file name is Projectile_816.xnb.

Just follow the guide to set up the mod pack and I'd be happy to answer any more questions or help in any way I can.