I think the context of the two videos you've posted here might be important. A rich and famous girl paid a lot of money to give her opinion about something that is expensive and obviously good. She says, "It's (tch) good." Another rich and famous girl in her own ridiculously expensive house talking all about herself and her wonderful, rich life in New York. Just before she gives her obvious opinions about everything being great...she clicks her tongue. It's so loud and obvious and yet others commented here that they didn't notice it. Really? Basically, it's rude to us too. The context is key. Making a rude sound before giving their own opinions...obvious opinions which aren't really unique. Clicking your tongue before giving an opinion like this...making a rude sound before you say something unnecessary, it lets others know that you know what you're about to say is useless. It's humble. It's self-deprecation. Clicking your tongue is not a thinking sound. It's not like saying hmmm. It's a way to humble a personal opinion, especially when you're giving an obvious opinion about something that is obviously good and other people are likely to be envious about. If you watch some of the other 73 questions videos you'll notice it more. For example, Blake Lively clicks her tongue before answering the best season is fall. SJP also clicked her tongue before saying the best season is fall. Could it be that everybody already knows that fall is the best season? Tay Tay clicks her tongue before saying coffee is her favorite drink...do other people like coffee? I could be wrong about this, of course. There might be other times when clicking your tongue is acceptable in the West. It could be a natural sound just when you open your mouth to start talking sometimes. We think clicking your tongue towards someone else or about other people is rude too. Rich people seem to do it a lot, though. Maybe they're pretending to feel bad about being rich? Trump doesn't do it (sniffle).

Well played, ma'am, well played.

Basically, が is the particle used to identify things. In this sentence, we're talking about Tanaka's book. We need to identify which one is his and we'll mark the location of that book in both the question and the answer using が. More here: http://www.guidetojapanese.org/learn/grammar/particlesintro

Well...this is a bit difficult. The basic answer is no, there is no difference. The practical answer is that you would only ever say (NO watashi wa...if you're talking about yourself, it's obvious and you don't need to especially point it out) genki desu (polite) and genki (casual). Da is the dictionary form. When you're speaking casual Japanese, you don't say the dictionary form. So, when it's formal (people you aren't close with) you say "Genki desu" and when it's casual (people you know well) you say "Genki!" Never say "genki da" because it's totally redundant. Just say "genki" when you're talking to your friends.