In short
Linewidth is the spectral width of the emission. Coherence length is how far the light stays correlated with itself. Narrower line means longer coherence.
The conversion between them depends on lineshape and on which definition of coherence length you use. Always state the convention.
Most applications need far less than the narrowest source on the market. Buy the linewidth your measurement uses.
In short
405, 488, 561 and around 640 nm cover most routine dye panels. Many systems add 445, 514 or 594 nm.
Specify power at the sample, then work backwards through your own optical path. Measured end to end transmission varies widely between systems.
Power stability and noise decide whether intensities are comparable between images, but the laser is only one contributor.
In short
Raman signal rises steeply towards shorter wavelengths. Fluorescence usually does too. The right excitation sits where that trade works out for your sample.
Common starting points: 532 nm for many inorganics, 785 nm for many organics, 1064 nm when fluorescence dominates. Verify on your own material.
For ordinary dispersive Raman, spectrometer resolution, not laser linewidth, sets what you can resolve.
