If I trust the fatwas of two different websites, is it permissible for me to adopt the easier of the two opinions, even if it contradicts the majority opinion? And is this considered following concessions (rukhas)? And is it permissible for me, as a laywoman, to adopt the opinion of Ibn Hazm or Sheikh Al-Uthaymeen regarding the issue of the wetness from a woman's private parts nullifying ablution, knowing that the majority of scholars say it does?

It is permissible to follow any of the muftis. So, if you act upon the saying of one who gives a concession, there is no blame upon you. However, it is not advisable to act upon the saying of one who believes that vaginal secretions do not invalidate ablution, because we do not know of anyone who held this view before Ibn Hazm, and it might be contrary to scholarly consensus (ijma').

Ibn Hazm is of the opinion that these secretions do not invalidate ablution, but the opinion that they do invalidate ablution is more cautious. If they are continuous, their ruling is similar to that of urinary incontinence: the woman purifies herself for each prayer after its time has begun, takes precautions (e.g., uses a pad), and prays, and whatever exits does not harm her prayer. If they are intermittent, she must wait until they stop. The fact that they are pure (not ritually impure) does not prevent them from invalidating ablution, similar to gas exiting from the anus.