Praise be to Allah.
No doubt it is obligatory for the Muslim to be a follower of his Prophet (blessings and peace of Allah be upon him) in what he prescribed and it is not permissible for him to go against that or to introduce any innovation into the religion, because of the evidence that indicates that it is obligatory to follow and it is forbidden to introduce innovation. But it should be noted that differing from the way of the Prophet (blessings and peace of Allah be upon him) and falling into bid‘ah may mean one of two things:
introducing an act of worship for which there is no basis in Islam, such as touching graves and seeking help from their occupants. The scholars call this real innovation (al-bid‘ah al-haqeeqah). This is that which was not prescribed at all.
the act of worship may be originally prescribed in Islam, and what is contrary to the sunnah may have to do with defining a certain time or place for it, or a certain number of times it is to be repeated, or the manner in which it is to be done or the reason for which it is to be done. This is called innovation by addition (al-bid‘ah al-idaafiyyah); it is not bid‘ah unless it is done regularly and repeatedly. If it is done only once or twice without adhering to that, then it is not bid‘ah, such as if people pray qiyaam (night prayer) in congregation (jamaa‘ah) on some occasion, without thinking that there is any particular virtue in doing so.
Hence ash-Shatibi (may Allah have mercy on him) said, discussing the “innovation by addition”: The word bid‘ah refers to an invented way of doing something in Islam that is similar to what is prescribed, of which the intention is to go to extremes in worshipping Allah, may He be glorified.
That includes regularly adhering to certain manners and forms of worship, such as reciting dhikr (remembrance of Allah) together in unison, taking the birthday of the Prophet (blessings and peace of Allah be upon him) as an Eid (festival), and so on.
It also includes adhering to specific acts of worship at specific times that were not defined as such in sharee‘ah (Islamic law), such as always fasting on the fifteenth of Sha‘ban (an-nusf min Sha‘ban) and spending that night in prayer (qiyam).
End quote from al-I‘tisam, 1/37-39
Adhering to a thing means doing it regularly and repeatedly.
Du‘a (supplication) is prescribed during the prayer and following it, according to the correct scholarly opinion. What is not allowed is reciting du‘a in unison. The evidence for it being prescribed to offer du‘a after the prayer is as follows:
It was narrated that ‘Ali ibn Abi Talib (may Allah be pleased with him) said: When the Prophet (blessings and peace of Allah be upon him) said the salam (greetings in conclusion) at the end of the prayer, he would say: “Allahumma ighfir li ma qaddamtu wa ma akhkhartu wa ma asrartu wa ma a’lantu wa ma asraftu wa ma anta a’lamu bihi minni. Anta al-muqaddim wa anta al-mu’akhkhir la ilaha illa anta (O Allah! Forgive me what I have done in the past, and what I will do in the future, and what I have concealed, and what I have done openly, and what I have exceeded in, whatever You know about me more than I. You are the One Who brings forward, and You are the One Who puts back, there is no god except You).”
[Abu Dawood]. This does not contradict the report that says that the Prophet (blessings and peace of Allah be upon him) said this du‘a before the salam. The Prophet (blessings and peace of Allah be upon him) used to recite this du‘a in both places. See: al-Majmoo‘.
It was narrated that Abu Umamah (may Allah be pleased with him) said: It was said to the Messenger of Allah (blessings and peace of Allah be upon him): Which du‘a is most likely to be heard? He said: “(That which is said) in the last part of the night and at the end of the obligatory prayers.” [al-Tirmidhi]
“at the end of the prayers” may refer to after the prayers or in the last part of the prayers. In the following hadeeth, for example, what is meant is after the prayer: ‘Uqbah ibn ‘Amir (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) instructed me to recite al-Mu‘awwidhat (soorahs that give protection) at the end of every prayer (i.e., after the prayer).
[Ahmad, Abu Dawood]
As for reciting du‘a in unison, there is no report that speaks of it; hence doing it regularly following the prayers comes under the heading of bid ‘ah.
So acts of worship must be done as prescribed by sharee‘ah in six ways: quantity, manner, time, place, reason and type. For more details of that please see the answer to question no. 21519
There is nothing wrong with reading Soorat al-Kahf on days other than Friday, if the reader wants to do that or if it so happens as part of his regular daily portion of Quran, and he will have a tenfold reward for each letter, as is the reward for reading other soorahs (chapters). But that is on condition that he does not set aside a special day for reading it, as is the case on Fridays, and hence he should not believe that reading it on this day is better than reading it on other days or that there is a particular virtue of reading it on a specific day that is like the virtue of reading it on Friday, because that virtue applies only to Friday, according to those who say that the hadeeth which speaks of that is saheeh (authentic).
And Allah knows best.