A. Use of 나 / 저:
I am talking about the main verb 좋아합니다.
You can use either 나 / 저.
나는 [or 저는] 좋아합니다. (✔)
What you can't use is 저는 좋아한다 (❌) or 저는 좋아해 (❌)
B. Conversion of verb to adjective
(자전거) 타는 follows the process of converting a verb into an adjective to describe the noun 것 :
자전거 타다 = ride a bike/bike-ride (verb) ->
자전거 타는 -> bike riding (adjective)
자전거 타는 + 것 ~ that which is bike-riding
나는 자전거 타는 것을 좋아합니다
= I like that which is bike-riding
= I like bike-riding
Ahh, ok, I mixed the ㄴ/는다 (impersonal) you wrote earlier with the construction with verb converting. It's that 좋아한다 I haven't grasped yet:p And thanks again for very detailed explanation. Whenever I hear or see 나는 I always expect very relaxed conversation among friends, so I was surprised to see the -합니다 ending which sounds so formal. But now I know it's at least possible if not preferable:)
나 is more versatile (can be used with all forms of verb endings) but 저 is preferred (not an absolute 'must') when it comes to politeness.
That said Korean being a pro-drop language where subjects are often omitted (especially in the 1st person). So don't spend too much time on this.