Let’s break down the first sentence, 私が飛ばせんのはコインだけじゃない. The sentence structure is A は B じゃない which means “A is not B”. は is the topic particle which indicates A is the topic of a sentence and じゃない is used to make a sentence negative.
First let’s look at the A 私が飛ばせんの which is a noun clause (= a clause which can act as a noun).
私 means “I”.
が is the subject particle. You might want to use は here but basically you have to use が to mark a subject in a subordinate clause, whereas は is used to mark a topic in a main clause.
飛ばせんの is a combination of a verb 飛ばせる meaning “can fly something” or “can shoot something” and the particle の which makes what comes before into a noun and it can be translated to “the one which”. In very informal speech, when the verb that ends in る is followed by the particle の, る often becomes ん as it’s a bit easier and faster to pronounce. For example, するの becomes すんの, 食べるの becomes 食べんの, 来るの becomes 来んの, and so on.
So 私が飛ばせんの means “the one which I can shoot”.
Now let’s look at the B. コイン means “coins” and だけ means “only” so コインだけ means “only coins”.
So the whole sentence 私が飛ばせんのはコインだけじゃない is, if it’s translated directly, “the ones which I can shoot are not only coins”. So it means “it’s not just coins I can shoot” or “coins aren’t the only things I can shoot”.
Now we’re going to look at the second sentence, これが私の全力だ.
これ means “this”.
が is the subject particle and this が is used to emphasise これ as Mikoto is showing THIS which is something Therestina has never seen.
私 means “I” and with the particle の, you can make it possession, so 私の means “my”.
全力 means “full strength”.
だ is used to make a sentence affirmative and declarative so it’s opposite to じゃない.
So これが私の全力だ means “This is my full strength”.