"The dog is sitting on the table."
Translation:कुत्ता मेज़ पर बैठा है।
How come you teach रहना in the 'tips and notes' section, but it does not allow for it in some of the sentences? It was never explained that we could also conjugate the way you have in this sentence with बैठा to also give the continuous tense. What's the difference between the two and why is रहना sometimes needed and at other times not?
The elements like जा रहा / चल रहा has the general sense of having remained in, being engaged in the action.
Some English expressions of present participial -ing form refer to present state as much as to continued action, e.g. to be sitting, lying, etc. These have as Hindi equivalents not continuous present forms but perfective participles of verbs denoting assumption of the given state, plus present tense forms of होना.
So, I am sitting. has the Hindi equivalent मैं बैठा हूँ। and I sit. has मैं बैठता हूँ।
As someone explained for another sentence where a similar issue came up, some verbs in Hindi just can't be continuous, and बैठना is one of them. For example, in English you wouldn't say "I am being hungry", you would just say "I am hungry". In Hindi hunger is expressed in the continuous form: "मुझे भूख लग रही है". On the other hand, while we can say "I am sitting", this sounds unatural to a Hindi speaker, who would just say मैं बैठा हूँ (I sit). Unfortunately these are things you just need to learn and retain. There is no real logic per se.