Can I pray Surah Kawthar in the first rakat and then Surah Ikhlas in second rakat? Or is it disliked because I skipped Surahs in between?
It is absolutely fine to miss two or more Sūrat in between.
However to miss one small Sūrah in between is Makrūh (disliked), but to miss a long Sūrah in between is permissible. So for example, to pray Sūrah al-Tīn in the first Rak’ah and to pray Sūrah al-Qadr in the second Rak’ah is permissible. However, to pray Surah al-Nasr in the first Rak’ah and to pray Sūrah al-Ikhlāṡ in the second Rak’ah should be avoided.
[Bahār-e-Sharī’at, vol. 3, p. 549 with reference to Al-Durr Al-Mukhtār, vol.2, p. 330]
Imam Ahmad Rida Khan (Allah have Mercy upon him) writes, “To miss out a small Sūrah in between is Makrūh; like to pray Surah al-Nasr and to pray Sūrah al-Ikhlāṡ, and to miss out a long Sūrah then there is no harm like Sūrah al-Tīn and Sūrah al-Qadr”
[Fatāwā-e-Ridawiyyah, vol. 6, p. 371]
Also, another ruling is that it is Makrūh to make the second Rak’ah longer than the first one. This is when the second Sūrah is longer by 3 verses or more. And if both Sūrah are equal in terms of number of verses, then the second Sūrah shouldn’t be longer in terms of number of words. For example, to pray Sūrah al-Inshirāh in the first and to pray Sūrah al-Bayyinah in the second is Makrūh though they both have 8 verses.
[Bahār-e-Sharī’at, vol. 3, p. 548 with reference to Al-Durr Al-Mukhtār, vol.2, p. 322]
Therefore, to read Sūrah Kawthar in the first Rak’ah and to pray Sūrah al-Ikhlāṡ in the second is permissible.
Allāh knows the best.
Answered by Mawlana Mohamed Husein Qadri