とする

Treat it like
Plain form verb/い adjective + とする
Noun/な Adjective + だとする

とする is used to make a supposition. とする represents a decision to assume.
Literally, it could be read as “Do like X is true”.
とする essentially means “Let’s behave like this is true, or consider it as…”.

This has a few applications, of which two are covered below.

Examples:

• 彼はいいひとだとする – To assume he is a good person.
• それはいいとして、進もう – Let’s just assume/treat it like its ok and move on. 

とされている

Is considered to be
Noun + とされている

とされる is とする is in the passive. As you should expect from the passive, it is a state of being “assumed”.
More simply, it just means “is considered to be”.
*Note this is technically N1? grammar but its easy enough to teach here.

Examples

• ニュートンは天才とされている – Newton is considered to be a genius.
• 彼女は女神みたいに美しいとされている – She is considered to be as pretty as a goddess.
• この寺は世界遺産とされている – This temple is considered a natural heritage site.
• 生き物は海から来たとされている – Life is considered to have come from the sea.

としたら・とすれば

If it is the case that..
Plain form verb/い adjective + としたら・とすれば
Noun/な Adjective + だとしたら・だとすれば

とする is frequently used with a conditional to talk about a hypothetical situation.
This pattern is typically used with a conditional like たら, ば, and less commonly と may be used.
This phrase is very similar to なら or だったら

Examples

• ゴキブリだとしたら駆除は大変だ – If it is cockroaches, getting rid of them will be difficult.
• 言わないと殺されたとしたら、しかたない – If you would have been killed if you didn’t talk, it was unavoidable. 
• 彼女が好きだとしたら、やってくれるかもしれない – If he does like her, he might do it. 
• 裏返るとすれば、明日だろう – If they’re going to change sides, they’re going to do it tomorrow. 
• 彼が犯人だとすると納得がいく – If he’s the criminal, then it makes sense. (natural conclusion)

たら and ば

Here is a quick review of the differences between ば and たら

• としたら places emphasis on the statement afterwards (When x is done then..)
  • 彼が犯人だとすれば、いろいろ納得がいく – If we assume he is the killer, then lots of pieces fall into place. 
    The statement is mostly about assuming that he is the killer.
• とすれば places emphasis on the statement before (If x is done…)
  • 彼が犯人だとしたら、凶器はもう海に沈んでいるはずだ – If he is the criminal, the murder weapon is probably already in the ocean. 
    This statement is mostly about the weapon being gone

として and としたら

Unlike として, which describes acting as if a false statement were true,
としたら・とすれば typically offer up a hypothetical situation, that may or may not happen.

• 自分の子供として育った – Raise as if they were my own child
• 自分の子供だとしたら育つ – I will raise them if they are my own child. 

とする・にする

There is one final possibility for とする that is not really relevant here, but could cause some confusion;
That the と is an adverbial replacement for に.
This is rarer, and happens with と adverbs or with some specific verbs.
I’m only going to explain it briefly here and may make another article on it in the future.

Examples

• 失敗となる – To become “failure”.
• 進むと決める – To decide to “move on”
• ゴロゴロとする – To rumble (rumbly do).
• 猫だとする – To decide ”is cat” (にする→とする）。
• 猫にする – To decide on cat.