今日は、貴方は何をしましたか?
私は公園に歩きました。 =私は公園に行きました。is better:) because you "went to" park, but if you want to say "I walked in the park" 私は公園を歩きました。;)
About the question, if this conversation is just between YOU and ME, no need to say 貴方and 私, because we already know "who" is talking to "Whom".
A: 昨日(Bさんは)何してたの?
B:(私は)公園で遊んでたよ。
However, if there is many people, we need to say "貴方" because we do not see "to whom". You can say 私 when answer the question, but it can dropp.″ 私=Speaker” so no need to say 私。
Talking with 5 people
A:貴方の好きな音楽は何ですか?
B:(私の)JAzzが好きです。
I think "私" has emphases meaning. Everyone use "私は~" When they want to say own oppinion.(Ex:私もそう思います・私は反対です・私は~~~~だと思いました。)
Daily life i think we are always dropping "私"
☆☆☆☆☆☆☆
私has two kind of means. ①for woman ②polite way. The first one, Woman always using 私 as you know, so man does not use it in daily life. However, 私 is polite way to say "I". Everyone using "私" when we are talking with VIP and When the meeting. Men is sometimes using 私 too:)
俺 is very agrresive i think, but my friend who is a boy using this one. 僕 is kid's using all the time, but my friend who is a boy using this one too:D
I think 俺 has kind of "Love myself or Pride of myself" way, because in Japanese we have a "俺様" word. 俺様 word means if someone very masterful, we say "He is very 俺様"
俺 is not rude, but maybe 僕is better than 俺 lol
I hope my answer will help your study.
keiko