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Hi,

(1) Can I use the verbs 'do' and 'perform' in contexts like "He did a <attribute> act/deed yesterday" and "She has performed many <attribute> acts/deeds in her life".... no matter the attribute means "good" or "bad"?

(2) Can I use the verb 'perpetrate' with the noun 'act'? (e.g., 'to perpetrate a good act') ... is that English very formal?

(3) Can I use 'carry out' with either 'act' or 'deed'? ( e.g., 'to carry out a good act/deed') ... the online collocation dictionaries i checked say nothing about 'carry out+act/deed'... on the other hand I remember seeing such use examples in some English corpora...)

Thanks for your kind comments!

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vlivef(1) Can I use the verbs 'do' and 'perform' in contexts

He did a good / an evil deed. - very very common
She performed an act of kindness. (The of-phrase is required).

You can see the various adjective collocations with deed here:

https://books.google.com/ngrams/graph?content=*_ADJ+deed&year_start=1900&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t2%3B%2C%2A_ADJ%20deed%3B%2Cc0%3B%2Cs0%3B%3Bgood_ADJ%20deed%3B%2Cc0%3B%3Bevil_ADJ%20deed%3B%2Cc0%3B%3Bsuch_ADJ%20deed%3B%2Cc0%3B%3Bgreat_ADJ%20deed%3B%2Cc0%3B%3Bquitclaim_ADJ%20deed%3B%2Cc0%3B%3Bheroic_ADJ%20deed%3B%2Cc0%3B%3Bnoble_ADJ%20deed%3B%2Cc0%3B%3Bvery_ADJ%20deed%3B%2Cc0%3B%3Boriginal_ADJ%20deed%3B%2Cc0%3B%3Bfoul_ADJ%20deed%3B%2Cc0#t2%3B%2C*_ADJ%20deed%3B%2Cc0%3B%2Cs0%3B%3Bgood_ADJ%20deed%3B%2Cc0%3B%3Bevil_ADJ%20deed%3B%2Cc0%3B%3Bsuch_ADJ%20deed%3B%2Cc0%3B%3Bgreat_ADJ%20deed%3B%2Cc0%3B%3Bquitclaim_ADJ%20deed%3B%2Cc0%3B%3Bheroic_ADJ%20deed%3B%2Cc0%3B%3Bnoble_ADJ%20deed%3B%2Cc0%3B%3Bvery_ADJ%20deed%3B%2Cc0%3B%3Boriginal_ADJ%20deed%3B%2Cc0%3B%3Bfoul_ADJ%20deed%3B%2Cc0

He performed a good deed. Emotion: no
He performed an act . Emotion: no

vlivef(3) Can I use 'carry out' with either 'act' or 'deed'?

It is rare, but used when the "deed" refers to a premeditated act of violence or war.

Hamlet accepts the duty of taking vengeance, but needs both to find an opportunity to carry out the deed and to convince himself that the ghost has spoken the truth and his uncle is indeed a murderer. 
Second, no matter what the objective socio-political conditions that might encourage recourse to assassination, there must be those who plan and carry out the deed. Is there then an archetypical assassin? 
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Many thanks for your help with my collocations questions, AlpheccaStars!
Since that subject still looks very complicated to me, if you could do me a favor and check whether the following examples are correct English?

1) Jim has nothing against committing acts of charity on behalf of his company.

2) A real Christian would never agree to perform an act of violence against his or her foes.

3) People sometimes do evil deeds just because they can not or do not want to tell the good from the bad.

4) Every time I perform a good deed I am happy :-)

Looking forward to your (finalizing!) comments...

vlivef1) Jim has nothing against performing committing acts of charity on behalf of his company.

Commit is nearly always associated with violent or illegal acts. He had a life of committing nefarious crimes of all sorts.

vlivef2) A real Christian would never agree to commit perform an act of violence against his or her foes.
vlivef3) People sometimes do evil deeds just because they can not or do not want to tell the good from the bad.

The attribute of "evil" means it is already judged to be extremely bad.

People sometimes do bad things inadvertently.