This article addresses more questions than suggested by its title (those mentioned in the title are the most relevant and common ones) and provides very few answers. However, the key aim of this article is exactly that – to shed some light to the aspects of Lithuanian prosody which have been at the periphery of linguistic research and which have only scarcely been discussed. There are three most significant questions and points of discussion, namely what constitutes the basis of a linguistic phenomenon known as Lithuanian pitch accent levelling and what difficulties occur in its linguistic analysis. Thus the study raises terminological questions, the relationship between different research paradigms (phonetic, phonological, perceptive) and the issue of the scope of empirical data. The second question addressed in the article is of a terminological nature, i.e. Lithuanian pitch accents or tones? On the basis of the typology of tonal languages, taking into consideration the state of the Lithuanian language, it is suggested that the term tone should be introduced to the terminology of Lithuanian linguistics. In addition, it is also proposed that some other terms should be introduced to refer to specific tones in Lithuanian traditionally referred to as the falling pitch accent (tvirtapradė priegaidė) and the rising pitch accent (tvirtagalė priegaidė). One of the suggestions is to use the terms acute and circumflex tones to refer to these Lithuanian prosodic phenomena. The third question is whether Lithuanian has pitch accents (or tones) in diphthongs. There is an established opinion that in standard Lithuanian pitch accents in diphthongal and mixed diphtongal syllables are clearly distinguished. This article provides phonological arguments which allow raising a working hypothesis that the status of the phonological prosody of diphthongs might be in need of reviewing. Alongside the conventional view that diphthongs feature a phonological contrast between the acute and circumflex, it is also possible to consider an alternative perspective which argues that the differential function in such cases is performed not by the prosodic element of pitch accent (priegaidė) but rather another prosodic element, i.e. stress. In principle, such an idea is neither original, nor is it new since it is based on the arguments of Jonas Kazlauskas which in this article are consolidated. This article does not draw any final conclusions but rather is an invitation to discuss these matters among the research community.