Of your three options, the first is wrong. You cannot say: He was seen do the test. If you use the verb do in this context, it requires the infinitive to in front of it.
Thus, it's correct to say: He was seen to do the test. This implies - without stating explicitly - that he was seen to have taken the whole test and completed it.
It is also correct to say:...
"My mother let me play today".
There is no passive here given as "was let". The verb allow must be used to give a passive meaning. let means allow. Please note: My mother allowed me to play today.
"I was allowed to play by my mother today".
The only passive use is when let means let out or rent, as is:
Who let the dogs out? [like the song]
The dogs were ...
The technically correct answer is
I was let to play by my mother
but let is not usually used this way and will sound awkward. It sounds so awkward that you should consider it incorrect to use.
A native speaker will probably think you're trying to say I was left to play by my mother.
You should say I was allowed to play by my mother instead.
Though the present simple is used, in all the sentences the part participle is working as adjective there.
No answer is given
It is given as an example
All items are provided
It is stolen property
Since past participle is acting like adjective in the examples, they give the impression that the activities are completed but they are not ...
 I think the question [that was given to me] is just about using an
 I think the question [that I was given] is just about using an
They have the same meaning but slightly different grammar.
In both examples, the bracketed relative clause modifies “question”.
The difference is that in  the recipient of the ...
Somebody gave me that
The above sentence is in active voice.
The structure is Subject + verb + indirect object + direct object.
When there are two objects , you can make any one of them a subject.
So the two passive voice sentences are:
I was given that
That was given to me
There is no difference in meaning but I was given that is natural
"The parcel appears to be opened" can only be understood as the present tense, and adding "... before it was revealed" cannot override this, it can only create confusion. The main verb "appears" is in the present, therefore "be opened" is also in the present, and nothing can shift it into the past.
Therefore you must say "The parcel appears to have been ...
(This is an old question ... but it was bumped, so ...)
Both the question and the given answer from @cbh have misunderstood the actual quoted text that's the context of the question.
As pointed out in the comment by @whitecap in this context 'opposed' is not fulfilling the function of a verb - therefore the title of the question ("oppose", active or ...