Regarding the first part and leaving out 'chunks' of words is because as long as something is obvious in the language you can leave some words out. For example, if someone was to say to me " ONamae wa nan desu ka? " since the question is directed at me i can simply reply " Cravez Desu " rather than saying " Watashi Wa Cravez Desu ". So again, if somthing is obvious you can leave some words out and is fine to do so.

If you take your example and 'Suki Desu', i think to be fair it would be harder to understand, since that there was no question involved. But again, since the boy is directly talking to the girl, apparent on tone and atmosphere saying 'Suki Desu' i think would imply that the boy means he likes her. It completely leaves it open to interpretation but if i was to be in that situation i would rather say " Watashi Wa 'Persons Name here' Suki desu " since it's a bit more of a personal matter than normal conversation.

Regarding the location-based pronouns etc. I understand what you are saying but again i think it is all based on what 'that' is. If 'that' was already a topic within conversation or if 'that' was gestured with hand movements (maybe pointing? but i heard they don't like to point over there) then maybe 'that' might be obvious within the conversation so 'that' doesn't need to be explained per say. Possibly harder for foreigners to understand but if it's normal in Japanese conversation and language then not much one can do in the situation but to ask them to clarify it a bit more.