35 degree diamond tool in LazyTurn. I haven't seen such a shape in the 1/4 in holder size
Can't be of much help on that statement other than grind your owne or check vendor sites to see what's available.
Even a 35 degree will not get into the very tight corners and you need a point tool with a radius on one or both sides such that it won't gouge the work. One should take into consideration the type of tooling to be used when designing a profile.
You can't select sections of a profile and the only way around that restriction is to use different dxf's files. Higher end programs will let you select the start and end points along a profile. Lt never went that far in development and thus it is what it is for the price.
I can't comment on some of your questions as i need to see some pic's. 
I would suggest you play with the rough and fine pass settings to get a handle on the pathing. The manual covers pathing.
Both LazyCam's SIM and LazyTurn insist on facing off the stock
No comment on LazyCam Lathe and strongly suggest you use LazyTurn.
LazyTurn insist on facing off the stock all the way to the center regardless of whether the spigots are shown or 
 not.
Note the attached pic and first few lines of the code below as it does not face it off to the center and starts on the outside of the profile with the spigots removed.
N15   G40G90    
N25  (Change to Tool: 35 DIAM 379 FLANK L                                                           -R0.0020-IC0.3790    Angle:00) 
N35  T0000 
N45  S402 F1.00 M3 
N55  G0Z0.0130 
N65  G0X4.8651 
N75  G1 F1.0000  X2.8611  
N85   X0.8311  
N95   F1.0000  Z-2.2533  
N105  G0  X2.8311  
N115   Z0.0130  
N125  G1 F1.0000  X0.8311  
N135   X0.8011  
N145   F1.0000  Z-2.2533  
N155  G0  X2.8011  
N165   Z0.0130  
N175  G1 F1.0000  X0.8011  
N185   X0.7711  
N195   F1.0000  Z-2.2533  
N205  G0  X2.7711  
N215   Z0.0130  
N225  G1 F1.0000  X0.7711  
N235   F1.0000  Z-0.1147  
N245   F1.0000  X0.7411  
N255   F1.0000  Z-1.6765  
N265  G0  X2.7411  
N275   Z-0.1147