俺 is a manly way to say “I or me”.
The particle の followed by こと means “about”, so 俺のこと means “about me”.
The を particle indicates the direct object of the following verb.
ずっと means “for a long time”, “all along”, or “forever” which is used when something is in the same state continuously.
許さなくていい is formed with the verb 許す meaning “forgive” and なくていい meaning “don’t have to”. So you use the nai-form of a verb, delete the い and add くていい to mean “don’t have to do something”. For example, “don’t have to go” – the nai-form of the verb “行く” is 行かない so it’s 行かなくていい. “don’t have to come” – the nai-form of the verb “来る” is 来ない so it’s 来なくていい.
The first clause お前がこれからどうなろうと is the subordinate clause which is “Aが どう + a verb volitional form + と” meaning “no matter how A does something”.
The A is お前 meaning “you”, which can be used towards inferiors or equals in a manly and friendly way.
これから means “from now on”.
なろう is the volitional form of なる meaning “to become or change” so “No matter how you change from now on”. In the anime it’s translated to “No matter what you decide to do” or “no matter what happens to you”.
And the second clause 俺はお前をずっと愛している is the main clause which is A は B を愛している meaning “A loves B” so 俺 (I) はお前 (you) をずっと (forever) 愛している means “I will love you forever”.