Yeah, FCP doesnt automatically change 60p to 24, if you drag a 60p shot into a 24p timeline it will just drop the unnecessary frames and it will play as a 24p shot, I used to just shoot everything in 60p with a 1/120 shutter but then I found that the footage looked weird once dropped into a 24p timeline with no speed change, the reason was the shutter speed not matching.
For slow motion I use cinema tools, just open the clip and hit the conform to 24 button pretty much.
I honestly think FCE should have 24p, unless it is a super old version. What you should try is setting up a timeline before dropping a clip in and see if you have the option. Just do comand+N for a new timeline and go into your sequence settings by clicking in the timeline (to make sure its selected) and hit comand+0 and make it a apple prores compression and click on the settings tab to see if you can change it to 24p.
PM me if you need any other help.