"I hope he'll stay by my side forever" and "I hope he'll stand by me forever" 讲得通，可是更普遍的说法是： I hope he'll be with me forever.

It is my wish, that he would be accompanying me always, standing close by my left side.

"I hope he'll stay by my side forever" "I hope he'll stand by me forever" First one sounds like the word said by a girl who want him together forever, but you can use it in general way. Second one is useful in many ways.

I wish he could stand by my left said forever

I will stand by him forever. Note: Although the Chinese says "he will stand on my left", that sounds strange in English. I am guessing that "standing on a man's left" means something special?