First, cutting something up with a razor blade is way too time consuming and not proper workflow in any version of FCP. In legacy FCP versions you should have been making Markers in the Viewer, and using them in the Browser as sub-clips. Way faster, easier, more organized.
In FCP X, in the Event Browser, you can select out ranges you want and apply either Keywords, or use "F" to make them Favorites. After creating a Favorite Range in a clip, you can change the name of that range (let view in the Browser), and add independent Notes (right click list header, add Notes, drag it over next to the Names column) to a clip's name, keword ranges, favorite ranges.
As for exporting just that segment, you have to do this, it's not as elegent as Legacy FCP, but it's how it works.
* Select a Clip in the Event Browser, right-click it and select Open In Timeline.
* Now it's in it's own Timeline and you can effect it, just like you did Master Clips in legacy FCP versions, just a lot easier and faster.
* At this point, you have two choices. Trip the clip and Cmd+E to export it, and it will only export the remaining section of the clip. But, be sure to restore it to its full length, or it'll only show up as this length when you drop it in other Timelines.
* Or you can use the Share menu to Send To Compressor, give it In/Out points, and export only that segment there.
As for P2 footage, once it's imported as ProRes, I've never had problems. The only issue could be applying effects and such before that specific clip has physically transcoded to ProRes. When you import like this, FCP X is reading the original data off your media card to allow you access to the footage right away. Only when that clip is fully transcoded will FCP X start pointing to the ProRes version. That's the only thing I can think of with P2 footage. That, and you don't have enough RAM, not a good enough Graphics Card, or are storing your footage on your system drive (a huge no-no).