「人間ができている」 means "(someone) is a mature person".
So you should parse it like:
A man [who is kind and at the same time mature], [like Yoshida-san]
「吉田さんのような」 connects to 「（優しくて、かつ人間もできている）男性」.
優しくて、かつ人間もできている modifies the noun 男性. 優しくて is the て form, ie the continuous form of 優しい, "is kind, and...". かつ means "besides" "...
Yes this is parsed as 広がって + きて + います. That is, the te-form of 広がる, followed by the te-form of the subsidiary verb 来る, followed by the polite form of the subsidiary verb いる. (て)くる is used very commonly in Japanese, and it does not necessarily describe physical movement. "To do X and then come back" is only one of the meanings of (て)くる. See: Difference ...
This is a combination of three grammar points, namely も, -てくる and sentence-end te-form.
It started to snow.
This てくる describes something is coming toward you, mentally, temporally or physically. Difference between -ていく and -てくる
It started to snow, and/so ...
This te-form is where "now that" came in. See: て form at end ...
The verbs are connected in て-form is to emphasize that you do A first before you do B.
連れて帰る means to bring and go home.
Some other examples are:
聞いて来る: To ask and come (ask and return; go somewhere else to ask is implied)
食べて帰る: To eat and go home
して見る: To do and see (basically means try)
連れて行く: To bring and go
The latter verb changes to Te-form too ...
Some context would help!
Anyway the も and て are sometimes used in that way describing a series of events, with a kind of an unstated tone of [Already this, I wonder what will happen next?]
So, the sentence in the title could eg come from someone who has first said:
The weather forecast really got it wrong this time. They said this was supposed to be a ...