You probably have "Save to file" switched on...so if you don't give it a new name everytime you playblast, it'll save over the previous one...now, if you still have the previous one open, it will say you are not permitted to use the file...a windows thing.
As far as only working when it wants to...well, this could be for a number of reasons. Firstly, get the latest drivers for your graphics card. What graphics card are you using? ...maya playblast is an opengl capture renderer. So, it is a rare problem, but it does happen that some cards do not work with it, or don't work well...again, usually remidied with new drivers.
also, check your visibility keyframes....new maya users usually follow the same bunch of tutorials...and the beginners tutorials, almost always start by telling you to save a keyframe by hitting the S key. This key sets a keyframe for every keyable attribute of your object...including visibility. So, if you have been turning things on and off using that attribute, while you are working in maya, it is possible you have accidentally saved keyframes, and therefore turned objects or groups on and off, and therefore, they will not display when you run a playblast. You can tell by displaying everything and hitting the play key in maya and seeing if anything dissapears. Then check those objects and their groups for keyframes (orange highlight on attribute and graph in the graph editor, and red keyframes on the timeline).
Also, make sure you hae View, and Show Ornaments switched on in playblast options, your frame range is not negative (start frame 40, end frame 1), and you have remove temp files ticked.
Also, if you are using windowsXP, it has a refresh problem with playblasts. Sometimes when the playblast is running, the maya screen suddenly goes blank...when you playback the playblast, it of course shows nothing but blackness. Most times, its fine if you just try again. Other times, you may need to free up some memmory on your c: drive. Just empty the recycle bin...of course, if you don't have much memmory to begin with...less than half a gb, you would think to restart your machine...there is a way around that problem until you can afford some more ram....go to your system tools, hardware manager, performance settings. In there, it has temp swap file (paging file) that can be used in a similar way to ram. By default, your system will be automatically controlling this...manually set it...if it has a pageing file set to c:...set it to 0mb to remove it. Then set a new paging file on another harddrive such as D:, and set it to a large figure, such as between 1gb and 3gb...if you have that available. Ok it, and restart. Your maya and playblast performance should be a lot better now. You need to constantly be aware of emptying your recycle bin, because every playblast you make will be deleted as a temp file unless you have chosen to save it...so it'll keep dumping huge files into your bin. Also, empty your system's temp directory, and your temp dir and temp internet files dir, in your profiles>documents and settings on your c:. A monthly defrag is also useful. Your system performance will be greatly enhanced by doing these simple things, and maya, and playblasts should be greatly improved.
For better playback in maya, set your animation settings to play "every frame". Now, this is what fcheck does...it plays every frame. It can't be ruled by a specific frame rate really, because its dependant on your system being able to stream that ammount of data that quickly. Comming off a scsi hard drive improves matters, as does more ram. However, when you want to slow it down to a 24/25/30 fps, you simply don't have propper control over it. You just have to do as you have been doing and using the playback controls to play slower and other software. Most of the time, its pretty much the right frame rate anyways, bar when it catches on the odd frame that is taking a while longer to load. It'll do.
I have never actually tried, but I suspect there may actually be frame rate controls as flags if you launch fcheck from the command prompt.