Can an infinitive modifies an adverb

His best form of expression in mockery is to laugh awkwardly

Since to laugh is an infinitive therefore it's a noun and adverb never modifies a noun
So in this case ; Is to laugh a verb ? Please clear this out .

Solution 1:

Since to laugh is an infinitive therefore it's a noun

This is inaccurate: "An infinitive may act as a noun". Interestingly, infinitives were originally included in the class of "gerunds" as they have a substantive quality about them:

To leave quickly would be a mistake. / Leaving quickly would be a mistake.

Here you can see the verbal nature of the gerund: they are modified by adverbs.

Compare this to a common noun:

A quick departure would be a mistake. in which a "real" noun is modified by an adjective.

OED

gerund, n. A form of the Latin verb capable of being construed as a noun, but retaining the regimen of the verb.

1542 Introd. Eyght Partes Speche sig. Ciii There be moreouer belongynge to the infinityue mode of verbes certayne voyces, called gerundes..[which] haue bothe the actiue and passiue signification.

(Current Modern English = "Moreover, there are certain parts of speech that relate to the infinitive of verbs: these are called gerunds, which appear in both the active and passive voice.)

You will see the OED reference to Latin - this is not too important as the reason is that in earlier times, English was supposed to be based on Latin - this is not the case.

It would have probably been better to call the gerund an infinitive as it does not have a tense, but this opportunity has been missed and English is stuck with infinitives and gerunds.