Thank you for~

That problem went smoothly, and thank you for your advice.
Thank you for singing for me. My feel feeling is getting better.
Yesterday was his birthday. so I gave him a gift,and he said thank you for the gift. →In my opinion, I think it's necessary to add the '' because you are quoting his words directly.
Thank you for all the great memories.

Thank you for~

[That problem went smoothly, thank you for your advice. ] A problem is not something good. Something which is bad can not go smoothly because "smoothly" is sometthing good. The way you wrote it sounds as if something bad was good which is contradictory. Here are some suggestions:

The problem was resolved and everything went well. Thank you for your advice.

(or) Thanks to yor advice, everything went smoothly.
Thank you for singing for me. [My feel is getting better. ] I am feeling better. (or) I am starting to feel better. This depends on what you mean. If you mean to say you were feeling ill, then now you are feeling better. If you mean to say that you did not know the song so well, then now you have a better feel for the song.
[Yesterday was his birthday. so I gave him a gift, he said thank you for the gift. ]

Yesterday was his birthday so I gave him a gift and he thanked me for it. (or) Yesterday was his birthday so I gave him a gift. He was very appreciative.

Thank you for all the great memories.