The probability of indirect human fertilization?
I don't have answers to all of your questions, but here is one example of a highly unusual conception via the gastrointestinal tract: http://blogs.discovermagazine.com/discoblog/2010/02/01/ncbi-rofl-thats-one-miraculous-conception/.

To cut a long story short, a woman born with a congenital defect that caused her to have no vagina was stabbed in the abdomen when her boyfriend found her performing fellatio on another man. She was taken to the hospital and patched up but a few months later:


  Precisely 278 days later the patient was admitted again to hospital with acute, intermittent abdominal pain. Abdominal examination revealed a term pregnancy with a cephalic fetal presentation. The uterus was contracting regularly and the fetal heart was heard. Inspection of the vulva showed no vagina, only a shallow skin dimple was present below the external urethral meatus and between the labia minora. An emergency lower segment caesarean section was performed under spinal anaesthesia and a live male infant weighing 2800 g was born…


The article concludes that:


  A plausible explanation for this pregnancy is that spermatozoa gained access to the reproductive organs via the injured gastrointestinal tract. It is known that spermatozoa do not survive long in an environment with a low pH (Jeffcoate1975), but it is also known that saliva has a high pH and that a starved person does not produce acid under normal circumstances (Bernards &amp; Bouman 1976). It is likely that the patient became pregnant with her first or nearly first ovulation otherwise one would expect that inspissated blood in the uterus and salpinges would have made fertilization difficult. The fact that the son resembled the father excludes an even more miraculous conception.”