Is it に indicating time?
No. ～にする has several meanings, and here it means "to choose~~" or "to decide on~~", not "to do at [point in time]". The に here cannot be "at (point of time)", since the に for "at [point in time]" cannot be used with から; you don't say 「～てからに + Verb」「*大学を出てからに働く」 to mean "Verb + ...
In this case, the particle "に" indicates specific time. It works the same as "に" in "8時に起きた" (I woke up at 8am.)
In your example, the skelton is "Specific timeに(劇団の仕事を)する" meaning "Do (the job in a theatre company) at specific time."
Japanese often puts relative time to this place. "大学を出てから" means &...
The short answer is that in the specific case of your sentences, the meaning is basically the same ('I like this cafe because it's cheap').
In the sentences, both から and て function to express a causal relationship between the predicates. However, this is not always the function of て when linking two predicates. It can also be used to express 'and', such as ...
Beware that this is a partial answer, and there are probably other differences to take into account too.
One key difference is that 〜て to express causality has a constraint: you can only use it if the second clause (after the て, 好きだ in your examples) is non-volitional, i.e. it does not include the intention or the will of the speaker, but it rather expresses ...
In this case, "て" in "寒くて" plays a role of "so". Here is an awesome article. Refer to the part 〜くて FOR "SO".
It's very cold so I can't speak clearly.
Next, "て" in "落ち着いて" works like adverbs. Also awesome article. Refer to the part て FORM FOR LINKING ACTIONS.
This is functionally same as this one: What exactly is this でね construction?
で is usually used to connect to phrases, but when the speaker is too excited about the first part already, s/he wants to affirm it with ね.
verb's te-form is used here, which is equivalent to noun/na-adj. + で (duh)
has です in the middle
The seemingly dislocated です is ...
The te-form and the masu-stem (aka i-form) are not the same syntactically. There are cases where they seem interchangeable, but in most cases, they are simply different. For example, only the masu-stem can work as a noun. You must use the te-form before a subsidiary verb (eg 飛んでくる, 歩いてみる), and you must use the masu-stem in a compound verb (eg 飛び出す, 歩き始める).