In english change means both the leftover money from a transaction and random coins in one's pocket. Is it the same in Russian? or is сдача just the leftover money.
In Russian, cдача is just the leftover money, not loose coins. In fact, this word means something like "payback" and can also be used do describe a reprisal if someone physically attacked you: "дать сдачи" = "to retaliate physically". However, be aware that unlike "payback" it cannot be used for a delayed retaliation and is not applicable to anything more serious than fistfights. It's a common schoolyard word though (at least it was when I was growing up).
Loose coins in one's pocket is "мелочь".
Is it a little rude to say this? Or another straightforward Russian sentence like "Дайте, пожалуйста"?
It would certainly be rude to ask for a change this way. On the other hand, I can easily imagine myself uttering it if I have just misplaced the change given to me and go through my pockets looking for it.
The intonation of 'моя' is in the wrong place, it makes it sounds like 'моё,' this is not to say that one can't hear the 'я,' one can, but the intonation is wrong. It makes it difficult for a person learning Russian to figure out just from the intonation because they would not realize the я is sounding like ë.