I read we can say: 1) He is sent for.
A few comments. "sent for" often appears in the past tense, for whatever reason, and so let's arbitrarily change everything to the past tense, just so it's clearer.
"He was sent for"
Okay. Next, in this case "sent for" means "summoned" or almost nearly "invited", which is a more common word.
"He was invited"
Okay, then can we say: 2) He is sent a student for?
Rewording this, as mentioned above
He was a student invited. *
He was invited a student. *
These are not correct. "by a student" fixes it.
Like, of course, we can say: 3) A student is sent for him.
Here, instead of "He was sent for...", you are saying "A student was sent for...". The object of the verb has changed. I think this is no longer the phrasal verb "send for". It is the standard verb "send". Like "A student was sent, to get the package."
But the idea is to make "he" the main figure in the sentence.
That could be "He was sent for, by the principal." However, it's sometimes considered good writing style to use the active rather than passive voice. "The principal sent for him." would be clearer.
Then if we can say those sentences we can improve the idea: 4) I was sent a present to by her OR 5) I was sent a present by her to *
Almost. Why "to"?
"I was sent a present by her" is alright. It would be better in the active voice "She sent me a present."
Further explanation - please also see Snowy Oz's answer about phrasal verbs. Essentially, there are two completely different words being discussed here, and getting mixed up.
2. send for.
These look like exactly the same word, with the second one just having a preposition, right? No, that isn't the case. Like "standing" and "outstanding" are two different words.
- send. The standard verb. "He sent the package". "He sent the package for/to John." In this case, "for" or "to" are normal prepositions.
- send for. The phrasal verb. "He sent for John." The word "for" is not a preposition. It's a particle.
From https://www.collinsdictionary.com/dictionary/english/send-for : "I've sent for the doctor. [VERB PARTICLE noun]" . Not [VERB PREPOSITION noun]
Some of your examples are using "send" (either with or without a preposition like "to" or "for"), and some of your examples are using "send for", which is the phrasal verb. This is similar to a German separable verb. "anrufen" may become "rufen ... an". The word breaks into two parts. "send for" is like "anrufen". One word breaking into two parts. The confusing thing is just because you see the word "for" appear, still doesn't guarantee which version of the verb it is. It could be the regular "send" and the preposition "for". Or it could be the phrasal verb "send for". And they are each different.