paul_c

Having a fairing has a big effect on aerodynamics. Don't forget, for a small rocket, its a significant weight though, so deploy it at the optimal time (which is, when the penalty in control/speed from aerodynamics is less than the weight penalty) - around 40-50km is a good guide there.
A rocket is controlled by 3 things: reaction wheel; RCS; engine gimballing. Its possible that engine gimballing has complete control over it - but only while engines are running. Reaction wheels convert electricity into control movements, and are needed once off the throttle. For orbital positioning, its very useful to be able to point it a direction with no throttle at all (for precision burns) so I'd always recommend at least some reaction wheel, although its interesting you got it into orbit without!
Full SAS controls is a bug in the latest version of KSP. It should be that OCTO has SAS, while the HECS gets prograde/retrograde controls too (I think....but we're going back a few versions now!)

Apologies, I didn't realise some of the probe cores had a small reaction wheel included - if that's the case, then no, you won't need the additional one.
ETA In theory, you don't need 4 solar panels either. It would be a brave soul who took 1 fixed panel. 2 is marginal, 3 guarantees solar power so long as its not nose or tail to the sun (leave it in normal/antinormal - pink marker - to ensure that). If you get to the stage of unlocking the deployable panels then 2 of these will 100% guarantee sun (1 will be 99% and I've seen it obscured!).
If the worst happens and you end up in the chicken-egg scenario of out of power, and no power/control to command the controller to turn it, timewarp ahead about 1/4 year and the sun will have shifted round with respect to the craft and it should burst into life again.

One way might be to "disable crossfeed" on the docking port(s), that way the delta V should be calculated only from the fuel it can reach via direct connections/its own stages etc. Docking ports are set to enable crossfeed by default, and stage separators are disabled by default.
Sometimes KSP won't calculate the deltaV of a craft with extra fuel/engines/whatever connected by docking ports, because it doesn't take into account that you might undock something to reduce weight and improve performance.