transfer learning with sentiment analysis?
I can not fully answer your questions, but would like to offer a couple of my thoughts here:
1) Transfer learning for sentiment analysis can be hard given that knowledge learned from one topic may not be not broad or general enough to perform well on the target or downstream tasks. For example, I have recently trained a neural network along with Word2Vec embedding using Twitter airline customer review data and get an prediction accuracy of 77%. However, when I use the same Word2Vec and neural network to classify some general customer review data, I got an prediction accuracy of only 35%.

2) Transfer learning in natural language processing is a hot topic and many researchers are working on it recently. 2018 sees some breakthroughs in transfer learning, i.e., Google Universal Sentence Encoder, BERT algorithm etc. I can not give you a comprehensive list here since I'm also learning. I would suggest you dive into some blog articles or even the original research articles to get a better understanding.

May it helps.