I wish I could go to the US to learn from native speakers > You should use' wish' when the possibility of you going is close to none or uncertain . 'Could' is used here not to indicate ' a past tense ' usage , but to indicate that it will not happened or being uncertain.
I wish I could be like him/I wish I could swim( for a non-swimmer)/I wish I had more time ( you didn't have)/I wish there were more ( not possible ).I wish you were here ( not possible)
I hope to study I can study in the US> hope indicate a possibility of happening ,and you want it to happen in the future . Can indicates the possibility .
I hope I'll be able to find true love> You want this to happen, and its possible / you can have the ability to find..
I wish I could find true love> You didn't and you know its not quite possible .
For expression fo goodwill or greetings , we used only ' wish" . > I wish you well / I wish you a "Merry Xmas"
Wish > use the past tense to indicate the unlikely situation
Hope > use the present tense to indicate possibility.
Hope with past tense > Only when you do not know what happened yet >I hope he left early ( you know he left , but early or not , you are still not informed .