There are some meaty questions. This is part of my field, and I'll do my best to answer them,
I am not familiar with theoretical approaches for modeling this reaction on the surface, but the reality is there there will be near 100% coverage with a monolayer, and in addition there will be "islands" that are piles of oligomers that are areas of increased thickness if you let it sit, say, overnight. If you use very very dilute conditions and/or short reaction times you can get less than 100% coverage, but that was never a goal of mine. Purifying the silane by distillation ahead of time can reduce these islands, but for some species they are just a reality. Again, it wasn't a feature that damaged my work when present. I wanted full coverage.
A typical set of conditions for attaching a tri-alkoxysilane to a surface would be 50 uL of silane in 20 mL toluene with a tiny amount of catalytic triethylamine. To get this reaction to work is trivially easy. To do it very precisely and repeatably does necessitate the use of dry reagents. It is also important to clean the surface thoroughly. I suggest sonications in hexane, acetone, water, then whatever your cleanest organic solvent is (isopropanol is often very clean). We would then plasma clean our slides with argon. I often did my silanations right on the bench in a slide holder with a top on, but for more precise ones we did them in a glovebox with dried reagents. And frankly the triethylamine was not used by many of my labmates, with perfectly good results.
I unfortunately do not know much about adhesion strength vs functionality, have you dived deeply into the literature on this one? I get the feeling there is some AFM work out there that could address your question, however it is a complex one. I punched "silane adhesion strength" into google scholar and got this one right off the bat "Chain Length Dependence of the Frictional Properties of Alkylsilane Molecules Self-Assembled on Mica Studied by Atomic Force Microscopy"
https://pubs.acs.org/doi/abs/10.1021/la950771u. It has been cited many times. I bet what you are looking for is somewhere in the family of articled citing or cited by such an article.