The park is free. Pay only if you want to enter the castle building to go up the viewing deck.

very easy on the osaka metro from namba: 1) Yotsubashi Line Nishi-Umeda (2 stops) starting at Namba Station to Hommachi Station 2) Chuo Line Gakken-Nara Tomigaoka (3 stops) starting at Hommachi Station to Morinomiya Station

It is published on the official site of Osaka Castle Park. The general vehicle parking lot seems to be in Mori no Miya and Osaka Castle Park station. I think that it is better to go by public transportation because it might be crowded.

It's about a 15 minute walk.

It's about a 15 minute walk.

You can buy a special ticket to the top of the Castle, That’s there you can view overall of the park.

大阪城を囲んでドライブは出来ますが　パーキングはあまりないので、やっぱり電車で来てゆっくり散策する方を　お勧めします。砂利道もありますから　歩きやすい靴の方が疲れません。

They close exactly at 5pm. I think they start not letting people into the Castle starting at 4:30pm (that's what the other castles and temples also did while I was in Japan).

I don't have the answer for your question. I have left the Osaka Castle a week back and it still have a lot of yaezakura flowers but the highlight for me is not the flower but the massive Oscaka Castle and the a very wide and deep moat. It makes me wonder how to conquer that castle without cannon.

Anytime from April through to June as far as the weather goes. Timing wise, early in the morning is less crowded so I would aim to get there around opening time to mid-day.