As I said, it is quite a good translation.
But you were right, there are some mistakes, and some things that could need improvement.
Though when it comes to chosing the right way to say it in English you really should better aks a native of that language.

Okay, let's begin.
"schenken" to "give" - you told me yourself that this isn't perfect. But all other expressions for it that the English language has doesn't seem to be normally used by natives, so you probably just should add a footnote and leave it at that.

"stay beside me" - I think normally one would say "stay with me".

"whatever you like" - leave the "ever" awyay, it's not really what the original line says.

"only love is all that counts" - is a bit too overcomplicated. Better say "only love is what counts" or "love is all that counts".

"today I'll give you a palace by Rhine" - I think a native'd rather say "by the Rhine" or "by the river Rhine"; not sure.

"that leads towards luck" - actually it's more of a new sentence, so maybe "it" instead of "that"? But "that" is okay, too. More literal would be "into luck".

"but only symbolic" sound a bit strange. Maybe "that's since it's just symbolic" or "it's just symbolic"?

"a true vow to faithful love" - "eisern" means "made of iron" or "as strong as iron", not "true" xD

"so, a palace can be seen by anyone"
"so" means "such", "also" would be "so".

"and the cathedral inspires awe" - that you got quite wrong.
"achtgeben" means "to take care"

"Ich schliesse unser Schloss
am Brückengitter an" is quite a strange phrase.
"anschließen" means "plug", "hook up", maybe also "attach". Try to make sense of that...
Well, the "Brückengitter" probably is the "portcullis".
http://en.wikipedia.org/wiki/Portcullis

"and still it isn't alone"

"in the Rhine" - maybe rather "into"? Dunno.

"Ich trage dich auf Händen" you also got wrong, it means "I carry you on my hands", and idiom meaning "I'll be gentle and careful with you and you are precious to me".