Is it permissible to recite Surat [chapter] al-Ikhlas between every four rak'as [units of prayers] of tarawih prayers, and send peace and blessings upon the Prophet between every two rak'as?

Reciting the Qur'an is unrestricted in the Shari'ah

In the Shari'ah, the command to recite the Qur'an is not restricted to specific times or circumstances apart from certain exceptions such as when a person is in a state of [janaba] major ritual impurity.

The virtue of Surat al-Ikhlas

The Prophet (peace and blessings be upon him) extolled the great virtue of Surat al-Ikhlas and recommended reading it at night.

Evidence from the sunna

- The Prophet (pbuh) asked his Companions (may Allah be pleased with them), "Is it difficult for any of you to read a third of the Qur`an in one night?" They asked, "How can a third of the Qur`an be read [in one night]?" He replied, "[Reciting] Surat al-Ikhlas is equivalent to [reciting] a third of the Qur`an" [Reported by Muslim through Abu ad-Darda`and al-Bukhari through Abu Sa'eed al-Khudri (may Allah be pleased with them both)].

- 'A`isha (may Allah be pleased with her) narrated that the Prophet (pbuh) dispatched a man at the head of a [military] company. He would regularly lead the company in prayers and conclude his recitations with Surat al-Ikhlas. Upon returning, the men mentioned this to the Prophet (pbuh) who told them, "Ask him why he does this." They asked him and he replied, "Because it [the sura] describes the Ever-Merciful and I love to read it." The Prophet then told them, "Inform him that Allah loves him" [Bukhari and Muslim].
The virtue of sending peace and blessings upon the Prophet (PBUH)

Sending peace and blessings upon the Prophet is one of the best acts of worship.

Allah Almighty always accepts it and it is the means for having other acts accepted. Just as the Prophet (pbuh) is the intercessor for creation, sending peace and blessings upon him acts as an intercessor for other righteous deeds.

Allah Almighty's command to send peace and blessings upon the Prophet is a general one. He says, "Allah and His angles send peace on the Prophet. So, you who believe, send peace and blessings upon him too."
[Qur'an 33:56]

General commands entail generality in terms of places, times, people and conditions. Therefore, whoever claims—without a proof—that sending peace and blessings upon the Prophet is prohibited at certain times, restricts what Allah Almighty has left expansive. This is because he restricts and particularizes what is general [in the texts] without proof. This is to be considered a kind of reprehensible innovation in and of itself.

The ruling

Based on the above, it is permissible and there is no objection to reading Surat al-Ikhlas and sending peace and blessings upon the Prophet in taraweeh prayers.

Allah Almighty knows best