Hello Donna and Buddaheart,
I'm not a teacher, not even close

. Just a regular grammar enthusiast.
I would say yes as the answer on " 1. Is "to develop grammar" an object complement? " . It is the complement of "them" .But it would be better if you didn't cut off postmodifer of "grammar" since it is also part of the complement which informs you what kind of grammar is in question.The whole object complement is "to develop grammar based on the linguistic input they receive". If you want to analyse the subordinate clause "which pre-programs them ..." , to my opinion it should be analysed like this :
Which - subject
pre-programs - verb
them- object
to develop grammar based on the linguistic input they receive- object complement
Now, if you want to analyse the object complement you can see that it is by form non-finite clause.You can transform it easily to its finite counterpart taking "they" as the implied subject (them being objective case of this pronoun in the original sentence)and make the analysis more understandable:
They develop grammar based on the linguistic input they receive.
they - subject
develop - verb
grammar based on the linguistic input they receive - direct object
If you analyse the direct object you see that it is a noun phrase by its form, with "grammar" as its head. The whole part after "grammar" is functionaly a postmodifier in the noun phrase headed by "grammar".
This postmodifier is an adjective phrase headed by "based" .The whole part after "based" is an adjective complement which is in this case obligatory since the adjective "based" and the following preposition "on" form one lexical unit. Precisely,adjective and its complementing preposition are inseparable since you will automatically add "on" after saying "based" in such contexts.( I suppose you will

).Of course, the bond between the adjective and its complement need not to be so strong and obligatory like it is in the case of "based on". So, "on the linguistic input" is an adjective complement by its function and a prepositional phrase by its form. (I've intentionally left out as part of this complement "they receive " as a postmodifier of "input" in order to shorten the phrase a bit. It is way too long

)
And of course it is true that : "There are verbs like "points to", etc. that seem to require a preposition after them to make sense" , exactly like this previous case with adjective "based on". As well as adjectives,verbs sometimes form a lexical unit (= logical unit) with its following preposition and they are then called "prepositional verbs". And yes,they are special,since the preposition (unless stranded) of this verbs is always followed by the prepositional object .
Best regards
Velimir