Question

How to do a RETWEET on an iPhone twitter app (MGTwitterEngine)

Answer 1

It seems that this function hasn’t supported in mattgemmell / MGTwitterEngine yet.

In the meantime, you can add that function to your current version of MGTwitterEngine by referencing this variant of MGTwitterEngine:
freeatnet / MGTwitterEngine

- (NSString *)sendRetweet:(unsigned long)updateID
{
  if (updateID == 0){
    return nil;
  }
  NSString *path = [NSString stringWithFormat:@"statuses/retweet/%u.%@", updateID, API_FORMAT];

  return [self _sendRequestWithMethod:HTTP_POST_METHOD path:path 

                        queryParameters:nil body:nil 
                            requestType:MGTwitterUpdateSendRequest
                           responseType:MGTwitterStatus];
}