Before answering your questions, be aware that the recommendation on what to read and what not comes from ijtihad of the scholars and madhhab views that some times are a bit narrow. This isjithad is based on qur'an and sunnah and the practice delivered or reported by the sahabah and tabi'yn.
Secondly what you recite of the qur'an during the prayer in principle is wide open:
-
Abu sa’id said:
we were commanded to recite Fatihat al-kitab and whatever was convenient (from the Qur’an during the prayer). (Sunan abi Dawod)
and in a long Sahih hadith you may find:
-
..."When you get up for the prayer, perform the ablution properly and then face the Qibla and say Takbir (Allahu Akbar), and then recite of what you know of the Qur'an, ... (Sahih al-Bukhari)
This means you could recite from the beginning of a surah and stop in the middle, you could start recitation somewhere in the middle and stop after some verses or you start at the last ten verses (for example) of a long surah and stop at its end.
However you may as stated above find some recommendations.
- Can you stop after 10 verses?
The answer as stated above is yes. But you must be aware that you should avoid stopping in a verse for which the meaning has not ended for example consider the sign in the moshaf represented by "لا" which indicates that one shouldn't stop recitation here for the reading of Hafs 'an 'Asim. See also What are the different punctuation in Quran?.
- If you read al-Fatiha and al-Kahf in the first raka'a should you read aal-'Imraan in the second?
Again here in general the answer is yes.
However the view of imam Malik for example is that on should follow the order of the qur'an, so if you read al-Khaf in the first raka'a you should either read again (later verses) from al-Kahf (or repeat the same verses) or move to the next surah for example Mariam etc. But doing it like you described wouldn't invalidate your prayer by any means. See also Correct order of surahs in prayers
- Is reading small surahs in the 3rd and 4th raka'a?
Well almost all madhhabs wouldn't recommend it in fard (obligatory) prayers, but there are ahadith reports showing that the prophet () would do this some times.
However as stated some madhhabs would regard it makrooh.
