You have misunderstood.
Offer can function as a catenative verb—that is, verbs that can be followed directly by another verb. Often, the second verb is a gerund. In other cases, the verb is an infinitive.
That is the case here: Tom offered [verb] + to drive [infinitive]
Wiktionary provides these similar examples (and many more):
He agreed to work on ...
There are many kinds of "accidents". A "car" accident is just one of them. So it would be unnatural to use "the car" right off the bat.
In fact, even if the first sentence was about a "car" accident, it would still be awkward to use "the car" in the second sentence:
I saw a car accident this morning. ??The ...
In addition to Jeffrey's answer I'd just like to mention that this is a pattern you might recognize from some pretty simple English phrases. Take, for example, someone that is tired and wants to leave a party:
I want to leave
Now consider your question, slightly changed:
Why can't we use "leave" instead of "to leave"?
You probably ...
"Christmas" is a noun. It is a proper noun, the name of the festival. It is capitalised because it is the proper name of the festival
Also "festival" is a noun in sentences like "There is a festival next week". Festivals are things. Many things are not physical things like "book", but abstract things like "...
The is a determiner - basically a demonstrative adjective - the means "that exact/particular noun of which we (speaker and listener) are [now] aware.”
(The is similar to “that” - in fact it is a form of the Old English “that” and often “that” can be used in place of the.)
The is used
(i) where the noun is well known to everyone:
"The moon is ...
They’re slackers, or someone “who shirks work or responsibility.” It is fairly informal, and in a different context can imply more than just laziness, as the other definitions from that link explain.
The manager, after inspecting the office, found that three employees were slackers and gossiped throughout the day.
I often “slack” or “slack off” on the ...
Example 1: Both occurrences of "books" should be "any books." As in "Do you have any books?"
Example 2: Both sides are OK. The answer might be better as "I don't have any books."
Example 3: The question should be re-written as "Do you have any books?" And the answer as "I have only one book."
You are laying too much stress on the distinction between the one- and two-word forms here.
sometime when your schedule permits
some time when your schedule permits
have exactly the same meaning.
It is true that unqualified "someday" and 'sometime" indicate an indefinite future time. It is also true that when qualified the two word ...