Here are my thoughts about those two questions of yours:
(1) Can the infinitive marker “to” be separated from the verb stem?
The matter of whether the infinitive marker “to” can be separated from the verb stem, as in “to clearly see,” “to confidently speak,” and “to thoroughly wash,” is simply part of the bigger issue of whether split infinitives should be allowed at all. This continues to be a controversial issue in English grammar, but I personally think that unless splitting the infinitive—or not splitting it—results in bad semantics, there shouldn’t be a debate about the usage at all. I split infinitives at will for stylistic purposes, but I’m also aware that splitting infinitives indiscriminately can be bad for prose.
Let’s take your first example of split infinitive: “to clearly see.”
Its normal unsplit form is, of course, “to see clearly,” and it works very well in sentences like “She wiped her eyeglasses to see clearly.” But when the sentence becomes more elaborate, particularly when the infinitive phrase needs to be modified with more words, keeping the infinitive unsplit becomes untenable. See and feel how unnatural this sentence sounds: “She wiped her eyeglasses to see clearly the lovely countryside at sunrise.” The sentence sounds much better with the infinitive split this way: “She wiped her eyeglasses to clearly see the lovely countryside at sunrise.”
Of course, another way to construct that sentence without splitting the infinitive is this: “She wiped her eyeglasses to see the lovely countryside at sunrise clearly.” The adverb “clearly” is, of course, meant to modify the infinitive “to see,” but this time it is so far detached from the infinitive as to seem to modify “sunrise” instead. It’s clear from these examples that splitting the infinitive is very often a semantic and stylistic decision rather than a grammar decision.
(2) The use of “whom” in modern usage
It’s not so much that the relative pronoun “whom” is often incorrectly used as that people tend to wrongly use “who” in place of it, and this misuse has got nothing to do with modern usage. The problem is that “whom” sentence constructions tend to sound too stiff and formal, as in “The salesman whom we hired for the new product is doing a terrific job.” The relative pronoun “whom” is, of course, the objective form of “who,” and is being used in that sentence to introduce a relative clause that’s functioning as the direct object of the operative verb "hired." What happens is that because of their discomfort with using “whom,” many people prefer to wrongly use the subjective pronoun “who” instead for such sentence constructions: “The salesman who we hired for the new product is doing a terrific job.” This misuse may be colloquially acceptable but strict grammarians continue to frown on it, so it’s highly advisable to avoid it in formal and academic writing.
Other than total reconstruction, there are actually two ways of avoiding “whom” in such sentences. One is, whenever semantically possible, to drop the relative pronoun altogether, as in this elliptical construction: “The salesman we hired for the new product is doing a terrific job.” The other is to use the relative pronoun “that” instead: “The salesman that we hired for the new product is doing a terrific job.” But conventional grammarians would object to this usage as well and insist that “that” should be limited to nonhuman antecedent nouns.
Personally, I wouldn’t hesitate to use “that” in such cases. After all, it turns out that early English actually used words related to “that” to mark relative clauses, and used “who” and “whom” only as question words and as indefinite pronouns in such constructions as “I wonder who were at the hunt.” Indeed, it was only because of the strong influence of Latin on written English in the 1800s that the contemporary use of “who” and “whom” as relative pronouns became the mark of educated people. This time, however, many native English speakers are rediscovering the grammatical virtues and simplicity of “that” as an all-purpose relative pronoun. I do think that even nonnative English speakers now can follow suit with little danger of being marked as uneducated yokels.
