TBH I haven't fully tested the player parser in v1.3. It is designed to use a b3d model that has all the running, skidding, falling, and whatnot all in one single file (not including the jump ball and spin dash, those are separate and do not go in the parser). So experiment with the parser is all I can say. It will be improved in the next release of BSFE. Just be sure to make a backup before you change it.
When it comes to reading a b3d model, Fragmotion is what you should use hands down.
When it comes to exporting a model, again use Fragmotion. Blender isn't the greatest when it comes to exporting stuff for Blitz3D. I hear it doesn't export vertex colors or any of the most basic stuff that nearly all major 3D editors support. That doesn't make it a bad modeling app, it just means it can't export into the formats Blitz3D supports very well. If you want full control of the model, you should use Fragmotion. Its free (Somewhat free; There are various irritations depending on the version you have which will bug you into purchasing it.) and it fully supports Blitz3D's native format. What you could do, is model in Blender, and export into a format Fragmotion can read, and then you can tweak the textures and other fancy stuff.
For the most part, though, people prefer to use one program for everything. I have a old version of 3DS Max that works perfectly with the Blitz3D pipeline, a plugin. Other people might prefer to use Fragmotion for everything including the modeling, especially because it supports B3D very well. Its up to you what you use, all you need to know is that Blitz3D supports the following 3 formats:
.3ds - Old as hell, been around since the 80's and has many hidden limitations. Remember MS-DOS? Well don't be surprised when your textures disappear and you are left scratching your head because texture names are limited to 8 characters like any file in MS-DOS!
.x - DirectX's native format. It has seen a few upgrades over the years, but it too is limited in what it can do and has plenty of flaws. Useful for basic, basic stuff.
.b3d - By far the best possible format you can use for Blitz3D. This format is Blitz3D's native format, and supports many great things like skin and morph that 3ds and x do not. You can also set material flags which let you define brush and texture effects within your 3D app; If you use x or 3ds, you have to use code to set flags like vertex color and alpha! The b3d format makes your model self-contained so that what you export is what you get back out when you load it up in Blitz3D.