The たら in the first sentence is more of a “when” than an “if”, so she’s saying that when she thoughtlessly turned on the TV in the morning there was some cartoon on (there’s nothing wrong with just translating アニメ as “cartoon”).
 
The second sentence isn’t complete, and it makes no mention of Rainbow Dash (the comment to the side is separate). The せいで structure isn’t always literally blaming a particular actor, she’s just saying “because I unintentionally ended up watching it till the end…”, with the implied conclusion being “I had to run to get to school on time”.
 
Now the が悪い structure in the side comment isn’t used literally to say RD is bad (let alone “the baddest”), and this one actually does assign blame. The translator also seems to have confused 全部 (all) with 全都 (the entire city). The sentence simply says “It’s all that horse’s fault!” Hope this helps.

The translation in the description is completely different from the one here >>580310
 
I don’t know what to believe anymore.

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