All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If you are unwell and it is difficult for you to perform each prayer at its prescribed fixed time separately, then according to many scholars, it is permissible for you to combine between the Thuhr (afternoon) prayer and 'Asr (late afternoon) prayer at the time of Thuhr or at the time of ‘Asr. Likewise, you should do the same with the Maghrib (sunset) and ‘Isha (night) prayers.
The method of combining the prayer is that you perform each prayer separately [at one of the fixed times]. After you complete one prayer with Tasleem (saying Assalaamu ‘Alaykum), you should then perform the second prayer. Thus, you may combine between the Thuhr prayer and 'Asr prayer, in a way that you first pray Thuhr and when you conclude the prayer by Tasleem, you pray the ‘Asr prayer.
You can combine the Maghrib and ‘Ishaa' prayers likewise, when you conclude the Maghrib prayer by Tasleem, you should perform the ‘Ishaa' prayer. However, it is not permissible for you to pray the two prayers with one Tasleem.
In case you combine the two prayers at the time of the second prayer [i.e. at the time of ‘Asr or at the time of ‘Ishaa'], then you may recite Athkaar (words of remembrance and mentioning of Allaah The Almighty) after the first prayer and pray the Sunnah prayer [the supererogatory prayer after the obligatory prayer] after it, before praying the second obligatory prayer. This is because praying the two combined prayers in sequence (without any break between them) is not a condition when you combine the prayers at the time of the second prayer.
However, if you combine the prayers at the time of the first prayer, then according to most scholars, you are obliged to respect the sequence [i.e. praying the second prayer straight after finishing the first prayer]. In which case, you should not leave a gap that is considered long according to the customs. Thus, you should not recite the legislated Athkaar after the prayer and you should not pray the Sunnah prayer after the first obligatory prayer. Rather, you should take the initiative to perform the second prayer, and when you finish the second prayer, then you may recite the Athkaar words of remembrance and mention of Allaah The Almighty that are recited after the prayer and then you pray the supererogatory prayers [that are performed after the obligatory prayers]. You may also perform the supererogatory prayer of the first obligatory prayer after praying the second combined obligatory prayer.
As regards doing what is called the 'Khatmah' on the occasions that you mentioned in the question, then this is not from the Sunnah (tradition) of the Prophet and so one should not do it.
As regards the supplication when completing the recitation of the entire Quran, then this is permissible but there is no specific supplication for it that is confirmed from the Prophet ; rather, a Muslim may say any supplication that he wishes.
With regard to supplicating at the end of the prayer, then this is from the Sunnah as well and many supplications from the Prophet were reported in this regard. Thus, if a Muslim supplicates with it, then this is good.
In any case, the most important supplication which a Muslim should abide by before saying the Tasleem (saying Salaam to conclude the prayer), is to seek refuge from the four trials as there is a difference of opinion about its obligation; so one should say:
• “O Allaah! I seek refuge with You from the torment of Hellfire, from the torment of the grave, from the trial of life and death and from the evil of the trial of the Antichrist.”
Among the supplications that were also reported from the Prophet are the following:
• "I seek refuge with You from the evil of what I have done and I seek refuge with You from the evil of what I have not done yet.” [An-Nasaa’i]
• "O Allaah, grant me an easy reckoning." [Ahmad, Al-Haakim; Ath-Thahabi and Al-Albaani: sound]
• “O Allaah, by Your knowledge of the unseen and Your power over creation, keep me alive so long as You know such life to be good for me and take me (cause me to die) if You know death to be better for me. O Allaah, make me fearful of You whether in secret or in public and I ask You to make me true in speech and fair, at times of pleasure and anger. I ask you to make me moderate in times of wealth and poverty and I ask You for an everlasting bliss and joy which will never cease. I ask You to make me pleased with what You have decreed and for an easy life after death. I ask You for the sweetness of looking upon Your Face and a longing to encounter You in a manner which does not entail a calamity which will bring about harm nor a trial which will cause deviation. O Allaah, beautify us with the adornment of faith and make us of those who guide and are rightly guided.” [An-Nasaa’i and Al-Haakim]
• Another supplication is the one which the Prophet taught Abu Bakr to supplicate with, which is: "O Allaah, I have indeed oppressed my soul excessively and none can forgive sin except You, so forgive me a forgiveness from Yourself and have mercy upon me. Surely, You are The Most-Forgiving, The Most-Merciful.” [Al-Bukhari and Muslim]
There are other numerous supplications that are reported before the Tasleem.
Finally, we recommend that you use a concise book of Athkaar (authentic words of remembrance and mentioning of Allaah The Almighty) like the book entitled Hisn-ul-Muslim, “The Fortress of the Muslim” in order to know what has been reported from the Prophet in this context and in other contexts.
Allaah Knows best.