Hi, You can take public transport, a ferry and then a bus to Preikestolen (the Pulpit Rock). The bus drops you at the start of the walk. The ferry and bus run fairly regularly with the bus waiting for the ferry. The walk up Pulpit rock is fairly easy, just 1 or 2 steep parts over some large rocks but it is a really nice walk with a stunning finish. It is possible to do it by yourself without a guide. The tourist information center will be able to give you more information or check online. You are going at the start of the peak season so you should find tour operators run regular tours at that time of the year. If you can afford it a car will give you freedom of choice but remember Norway has toll roads, ferries and gas that are all expensive so tours may be cheaper in the long run.
The other walk you mention, the 4444 steps I haven't heard of sorry so I am of no help. You will need a car (or tour group) to get out to the start of the walk to Kjeragbolten as I couldn't find any public transport way of doing it last summer. It will be a 2-3 hour drive from Stavanger.
Another possible walk/outing would be to Månafossen. It is a large waterfall with a nice walk into a boulder field and picnic spot by a lake that is accessible from Stavanger by public bus (takes close to 2 hours, 60km from town). Norway is beautiful, Stavanger is stunning! Walk around old town and see the church, well worth the visit on top of getting out into the nature :-)
