or can you simply say
タクシーは高いから without the
As Tomiyoshi notes, です is a polite marker, much like the -ます ending on verbs. The plain form is だ, corresponding to the dictionary or plain form of verbs. In technical terms, this です・だ word is often called a "copula" (after -i adjectives, です is instead regarded as a politeness marker). Whether either form is required at the end of a sentence depends on two things: 1) the grammatical structure, and 2) the social register (i.e. the context, who you're talking to).
Generally speaking, if a sentence ends in a noun or a -na adjective, you need to use the copula (either だ or です, depending on social register).
If a sentence ends in an -i adjective, as in your sample sentence, adding だ in informal contexts is actually considered incorrect grammar, since the -i adjective is already grammatically complete on its own. In technical terms, an -i adjective forms a complete predicate (i.e. it works as a verb), so the copula is not needed. However, ‑i adjectives do not conjugate for politeness (there is no -ます form), so in polite contexts, です is used as a politeness marker, as a kind of replacement for -ます.
If you're among friends, だ after nouns or -na adjectives might be appropriate as the less-formal plain form. If you're among strangers, colleagues, or in a professional setting, you should use です, also after ‑i adjectives.
Yes, it's grammatically correct. です is just a polite expression. I would prefer to add です when I am in a formal situation or with senior people.
Not necessarily. It depends on how polite you want to be.
Yes, both are correct. You can say:
because these are inverted sentences of:
(You don't say *バスに乗りましょう。タクシーは高いからです。/*バスに乗ろう。タクシーは高いからだ。 because you don't say *タクシーは高いからです、バスに乗りましょう。/*タクシーは高いからだ、バスに乗ろう。You'd use タクシーは高いからだ。/タクシーは高いからです。 when you say "It is because taxi is expensive", as a response to "Why do you take a bus?" etc.)