Time needed to see Iwakuni

how many hours I need for visiting iwakuni (bridge, castle etc...). are 3 hours enough?

Using public transport?
Or using own car?
Want to take photos?
Or walk around also?

Transportation between the station and the bridge is around 20 minutes one way. Altogether, I would calculate an hour for non-sightseeing activities, such as orientation and transportation.
The bridge requires 20-30 minutes.
The castle adds about 60-120 minutes. The ropeway will be out of service during April and July, in which case it will take considerably longer.
As for the "etc.", you have to be more specific.

For just the bridge and the castle, three hours can be just enough if you travel at a relatively fast pace and make no mistakes along the way.

We visited the area a few years ago, and spent about 4 hours visiting the Kintai-kyo Bridge, Iwakuni Castle
and Kikko Park.

Thank you! The time I am calculating is only for visiting the area, not for the transports.
So, in 3-4 hours I can visit at least the castle, the Kikko Park and the bridge, right? What else to do?

Another question... I am planning to visit Iwakuni in April, any alternative to climb the hill? I do not want to waste too much time. Is it easy to find a taxi?

What else to do?

By the time we finished visiting the castle, we spent 10 mins viewing some rare snakes in front of the ropeway entrance, and that was the end of our Iwakuni visit. Hopefully, others would provide you with additional information.

any alternative to climb the hill? I do not want to waste too much time. Is it easy to find a taxi?

I am sure you would be able to walk to the castle, but unsure if you would save any time. Ropeway seems faster.

I noticed taxis at both shin-Iwakuni station as well as near Iwakuni bus stop, but very few.