I'll tackle this part of the original post.
I play only occasionally with blues and jazz lineups. I've played rock, blues, swing, motown, reggae, ska, calypso, and other grooves in bands previously.
I keep a master songlist of all my favorites from all my bands and gigs. I also have a Casio keyboard in my practice area with 50 or so drum samples. Not super high quality, but good enough for practice.
Example: I'll put on the "latin" drum sample at 140 bpm or so, and start grooving on the changes to "Blue Bossa" or "Song For My Father". Then maybe I'll work on playing the melodies to these pieces, and then maybe improvise over the changes.
The "swing" sample is great for practicing walking basslines, either over 12 bar blues, or any other tunes with a swing feel. I also practice soloing over this feel, as this seems to be what I get called on most often to improvise over.
Another exercise involves running diatonic arpeggios, with extensions up to the 11th (so far). For this I use a simple drum pattern and raise the tempo gradually (4 bpm increments). This helps with theory, physical coordination, and staying relaxed under the stress of uptempo grooves.
The strong groove is my inspiration no matter the style, so basically I try to create an accurate rhythm section with my drum sampler. From this practice, when I do play gigs or jams, I can hold down the groove no matter what (kind of nonsense

) is happening on the front line.
I hope this is helpful...somehow.