Self-supervised learning (SSL) speech representations learned from large amounts of diverse, mixed-quality speech data without transcriptions are gaining ground in many speech technology applications. Prior work has shown that SSL is an effective intermediate representation in two-stage text-to-speech (TTS) for both read and spontaneous speech. However, it is still not clear which SSL and which layer from each SSL model is most suited for spontaneous TTS. We address this shortcoming by extending the scope of comparison for SSL in spontaneous TTS to 6 different SSLs and 3 layers within each SSL. Furthermore, SSL has also shown potential in predicting the mean opinion scores (MOS) of synthesized speech, but this has only been done in read-speech MOS prediction. We extend an SSL-based MOS prediction framework previously developed for scoring read speech synthesis and evaluate its performance on synthesized spontaneous speech. All experiments are conducted twice on two different spontaneous corpora in order to find generalizable trends. Overall, we present comprehensive experimental results on the use of SSL in spontaneous TTS and MOS prediction to further quantify and understand how SSL can be used in spontaneous TTS. Audios samples: https://www.speech.kth.se/tts-demos/sp_ssl_tts.