Maybe. It depends on what the writer is trying to say. If the writer means: - I hope you are well. - And I hope you are looking forward to your stay at my place. the sentence is fine. If the writer means: - I hope you are well. - And I am looking forward to your stay at my place. then it needs to be changed to "I hope you are well and am looking forward to your stay at my place." or "I hope you are well and look forward to your stay at my place."

Neither. The sentence is perfectly correct and natural. It's a condensed form of this: I hope you are well and [ that ] [ you are] looking forward to your stay at my place.... There is no need to repeat 'you are'.

Hi This is fine :) Jason