Úszok and úszom is also correct but without an object. In this sentence the correct solution is the úszok. Definite, indefinite conjugation. Indefinite conj.: úszok - I swim. Definite conj.: úszom egy hosszt: I swim the length of the pool. The definite conj. requires always an object.
According to Wiktionary, úszik is a strictly intransitive verb (as would make complete sense considering it really is impossible to "swim something", but úszok and úszom are optional in the 1st person. If it really had both indefinite and definite forms, they'd list forms like ússza and ússzuk, wouldn't they?
Yes, you're right, the "úszik" is an intransitive verb. But in this case there is a special type of verb. This conjugation according to another rule. This is the so- called "ikes ige". Its conjugation is different from the normal conjugation. This is a very complicated subject, and many native Hungarian conjugate these verbs in different ways. I would not force this issue at this level of the Hungarian language learning. I am a Hungarian native speaker, please believe me :)
Very good question, you clearly deserve a lingot!
The answer is: in this sentence the adverb "egyedül" stands in the Coda, where the less important sentence constituents are placed.
Instead, if you move it before the Verb, which is the Focus position, it becomes the most important part of the sentence with a big emphasis on it.
(There is a very good summary of these things by vvsey here: https://forum.duolingo.com/comment/20169609/Structure-and-word-order-of-a-Hungarian-sentence )
Holsen4 "Oftentimes", and "oftimes", are both one word, i.e., not separated. And I speculatively suggest that those words are too elegant for a translation into English of this straightforward Hungarian sentence; at least, it would be too labor-intensive to include them in this course.