Is it permissible for a Muslim who does not adhere to a specific madhhab to choose from the four madhahib that which is easier for him in acts of worship, such as adopting Imam Ahmad's view that prayer is not invalidated by clearing one's throat, knowing that Imam Malik does not permit this? And is he required to repeat the prayer in such a case?

The fundamental principle is that a Muslim should follow what is indicated by the Quran and Sunnah. As for the layman who is unable to comprehend the evidence, he should consult the people of knowledge.

If the opinions of muftis differ for a layman, there are various scholarly views on this matter:

Choice (Takhyeer): The layman may choose whichever of the two opinions he wishes. This is the view of some Shafi'is and Hanbalis. No Choice (Tarjeeh - Prioritization): One must prioritize between the opinions. This is the view of the Hanafis, Malikis, and most Shafi'is. Prioritization may be done by: Adopting the opinion of the most knowledgeable and pious scholar. Adopting the stricter opinion. Adopting the lighter opinion. Adopting the opinion with stronger evidence. Consulting a third party.

The prevalent fatwa is to prioritize based on the mufti's knowledge, piety, and God-fearingness, and not to follow the easier opinion merely because it is easier.