Not all words in Esperanto correlate to a similar sounding word in English. "Taksi" is one of them, so you'll just have to memorize it. It's meaning is to rate, to appraise, to estimate. "Pensi" is to ponder, to contemplate, to ruminate. Both might be translated as "to think" but their meanings are quite distinct.
After surfing round wiktionary quite a bit (taksi really does mean taxi in quite a lot of languages) I'm pretty sure it's from the Latin taxō (“I handle, estimate, judge”) and related to words about tax in a number of European languages. For instance: https://en.m.wiktionary.org/wiki/taksa
My impression is that "taksi" is more like an assessment or a valuation. In this sentence Adamo is assessing the risk and concludes that it is dangerous. In Dutch we have the word "taxeren", which means to estimate the value of something e.g. to assess the value of a house or a car.
Adamo taksas, ke estas danĝere.
Adamo thinks that it is dangerous, the action or whatever, it is not specified what we're talking about, it is just a general statement, thus without a pronoun.
Adamo taksas, ke ĝi estas danĝera.
Adamo thinks that it is dangerous, here it is a specific it, it might be the spider under his bed or it might be the basilisk standing on his lawn, but it is commonly understood by the speaker and the listener as to what this it refers to.
"Adam thinks that he is dangerous" would be "Adamo taksas ke li estas danĝera". Your interpretation is not possible for the given sentence for two reasons, which are both discussed in the thread started by tvoiles (please read vikungen's post).
I don't understand your question: verbs do not really refer to anything. And what do you mean by an "it" without a pronoun?
in the sub clause, or second clause (I don't know the term), 'ke estas dangxere' there is no pronoun, so the subject of the sentence is implied. My question was, why an implied 'it', but not an implied 'he', but I see vikungen has answered my question. Estas on its own is always a general statement, with no pronoun implied, is that correct? In some languages it would be very ambiguous to have a verb without a pronoun, as it could be interpreted as referring to an it, he, she, or even they.
Yes, you understand it correctly: estas without a pronoun always refers to an empty subject (or as it is also called, dummy pronoun 'it').
This means that you cannot drop the pronoun subject in Esperanto, as you do, for example, in Italian or Greek. But that should be clear first of all from the fact that Esperanto verbs don't conjugate...
I can understand why the word it does not need to be translated in sentences such as "It is raining", as it does not stand for anything in that sentence, but in this case Adamo must have had something in mind when he spoke about it being dangerous, whether is was something physical (e.g. a shark),
- Adamo taksas, ke ŝarko estas danĝera
or an activity (e.g. to jump off a cliff),
- Adamo taksas, ke estas danĝere salti de klifo
In English, we'd represent that something by it, but can that the equivalent always be omitted in Esperanto if the listener knows what is is being talked about, as is presumably assumed to be the case in this sentence?