Expressions – Listen to Music or Listen for Music: Proper Usage

Yes, constructions such as

• The series will continue tomorrow evening.
• The show closes next Wednesday night.
• The package arrived on Christmas morning.

are quite common.

For night, it is more customary to say last night rather than yesterday night, although we do say yesterday evening, tomorrow night, Saturday night, and so on.

When the day is itself a compound, I think this compact form is less common, however. To say

We should arrive the day after tomorrow morning

sounds unnatural to me; my eyes jump to the set phrase "tomorrow morning," and then I wonder how there can be a full day after a part of a day, and then I realize I have parsed it wrongly. Better to have said

We should arrive the morning of the day after tomorrow.

What you're confronting here is one of those fiendish composite verbal constructions English employs with relish to keep schoolchildren, their teachers, grammarians of every stripe, and speakers of non-English languages of the Wrong Sort^† in their respective places.

The construction here is [look forward to]. This must be carefully distinguished from the collocation [look (vb) + forward (adv.) + to (inf. marker)], which is how your first sentence must be construed:

My grandparents are looking forward to celebrate my arrival in February. = “My grandparents are directing their [figurative] gaze into the future, so that they may celebrate my arrival.”

Look forward to, employed as a fixed phrase, is a “phrasal verb”. It is transitive, taking a substantive — a noun, a pronoun, or a noun phrase — as its direct object. It may be glossed as “happily await” or “expect” or “anticipate”:

I look forward to Christmas. = “I await Christmas happily.”

There are two forms of a verb —celebrate, in your examples— which may act as a noun, and thus as the direct object of a verb such “to look forward to”:

• “to VERB”, which is called the *marked infinitive” because the bare infinitive of the form “VERB” is marked with the particle (not preposition) “to”, or
• “VERBing”, which when used this way is called a gerund because that’s what students of foreign languages of the Right Sort^† call it.

But even English has to draw the line somewhere — “look forward to to” is just too awful (in any sense) to contemplate. Consequently, look forward to takes the gerund, as in your second sentence:

My grandparents are looking forward to celebrating my arrival in February. = “My grandparents await, happily, celebration of my arrival in February.”

There's far more to parsing this insidious phrase; but you need not yet be troubled with the descriptive grammarians' cunning distinctions between prepositional and particular phrasal verbs. And you certainly don't want to be involved yet with the difficulties of transforming this sentence, into which you may be drawn if your editor is of an Enlightenment persuasion and deprecates ending clauses on a preposition because that's not done (nefas) in other languages of the Right Sort^†. It takes an iron determination (and a strong stomach) to come up with constructions like this:

We celebrate my arrival in February, forward to which my grandparents are looking.

In any case, the celebrate in your first sentence is not Future Simple, and the celebrating in your second sentence is not Future Continuous; they are, respectively, an infinitive and a gerund.

^† The Right Sort of non-English language embraces the Greek of Pericles, the Latin of Cicero, and possibly the Hebrew of Moses, who may be regarded as a British Israelite denied the opportunity to realize his Britannicism (just as was he prohibited from entering the Promised Land — in fact, the two may be the Same Thing). All other non-English languages are of the Wrong Sort.