Minecraft – Why won’t the horse show hearts when tamed

Mods will be compatible as long as they don't overwrite the same files in minecraft.jar. You can check this by looking at the class files in the mod (that have obfusticated names like a.class or bg.class, and you need to put into minecraft.jar) and checking that there's no overlap between the two lists of files.

Slimes can only spawn in chunks where they are allowed. Why are there slimes in chunks that shouldn't have them?

1. Slimes move around. Chances are this is what happens. They will bounce (ooze? slide?) to different chunks over time. This can include falling from higher heights.

2. You used or read the slime chunk calculator wrong. Maybe you punched in the seed wrong or chose the wrong map. Maybe you misread your map? Double check you if you needed to have a "-" (negative sign) on your coordinates. Double check your calculator.

This may or may not apply to your spawning pads but slimes can spawn at any light level, unlike other mobs like skeletons, zombies, etc.

For reference: Minecraft Wiki - Slime http://www.minecraftwiki.net/wiki/Slime