Technically, this の is not a particle but a special noun known as explanatory-の. If you aren't familiar with this yet, you have to learn it first. Although there is no direct equivalent in English, this is very important when you want to speak Japanese naturally.
When this type of の appears in a question, it seeks clarification (or explanation, excuse, etc). You need to use this type of の every time you make a question about what's already going on now.
- Question Markers: か and の
The connotation that the の has is to seek clarification based on background contexts, while the か doesn’t require any context.
何見てるよ is incorrect because it doesn't even look like a question.
In speech, の is very often used with various sentence-end particles, so you'll see variations like のさ, んだぜ, のよ, んだわ, and so on. It is true that "bare の" is relatively specific to feminine or childlike speakers in fiction, but other types of speakers do use explanatory-の as part of more complex sentence endings. For example, in a situation where a small girl might say 犬が好きなの, other characters might say 犬が好きなのよ, 犬が好きなんだ, 犬が好きなんです, 犬が好きなのさ, and so on. These all translate to "(It's that) I like dogs".
