Перед работой я быстро побрился новой бритвой, а потом понял, что забыл часы.

The preposition перед normally takes the instrumental case when it means before / in front of.

So:

• работа → nominative
• работой → instrumental singular

In time expressions, перед + instrumental means before something:

• перед уроком = before class
• перед сном = before sleep
• перед работой = before work

So this is just the normal pattern required by перед.

Yes, Russian often omits subject pronouns when they are clear from the verb form.

So both of these are possible:

• Перед работой быстро побрился...
• Перед работой я быстро побрился...

The verb побрился already shows masculine singular past, so the subject is often understood.
However, я can still be included for clarity, emphasis, or simply because it sounds natural in context.

In this sentence, я is not required, but it is perfectly normal.

This is an aspect question.

• брился = imperfective
• побрился = perfective

Russian often uses the perfective when talking about a completed action in a sequence of events.

Here the speaker is describing completed steps:

1. He shaved
2. Then he realized something

So побрился fits well because it presents the shaving as a finished event.

Compare:

• Я брился = I was shaving / I used to shave / I shaved (focusing on the process)
• Я побрился = I shaved, completed it

The ending -ся here shows that the person did the action to himself.

• побрить = to shave someone/something
• побриться = to shave oneself

So:

• Я побрил брата = I shaved my brother
• Я побрился = I shaved

In English we usually just say I shaved, but in Russian the reflexive form is often needed to show that the subject is acting on himself.

Because Russian uses the instrumental case to show the tool or means used to do something.

• бритва = razor
• новая бритва = a new razor
• новой бритвой = with a new razor

So побрился новой бритвой means shaved with a new razor.

This is a very common use of the instrumental:

• писать ручкой = to write with a pen
• резать ножом = to cut with a knife
• есть вилкой = to eat with a fork

Because с usually means with in the sense of together with, not necessarily using as a tool.

Compare:

• побрился новой бритвой = shaved using a new razor
• был с новой бритвой = was with a new razor / had a new razor with him

So for the instrument used to perform the action, Russian normally prefers the instrumental case without с.

Russian word order is fairly flexible, and adverbs like быстро can often move around.

These are all possible, with slightly different emphasis:

• я быстро побрился
• я побрился быстро
• быстро я побрился (more marked, more emphasis)

The version я быстро побрился is very natural and neutral. It simply means he shaved quickly.

Both а and и can connect clauses, but they are not identical.

• и = and
• а = and / while / but, often with a mild contrast or shift

In this sentence, а потом feels like a natural transition to the next event:

• first, he shaved
• then, something else happened

There is a small sense of moving to the next stage of the story. Russian often uses а this way, even when English would simply say and.

So а потом понял... is very natural narrative Russian.

Because что introduces a subordinate clause.

The structure is:

• понял = realized
• что забыл часы = that he had forgotten his watch

Russian normally puts a comma before что in this kind of sentence:

• Я знаю, что...
• Он сказал, что...
• Она поняла, что...

So the comma is required here.

Again, this is about aspect.

• понимал = was understanding / understood in a general or ongoing sense
• понял = understood / realized at a specific moment

Here the sentence describes a moment of realization:

• first he shaved
• then he realized something

So понял is the natural choice because it marks that sudden completed moment of understanding.

Because забыл is perfective and refers to a completed fact: he came to realize that he had forgotten the watch.

• забывать = to forget habitually / to be forgetting
• забыть = to forget, as a completed event

Here the meaning is not a repeated habit like I often forget things. It is one specific event, so забыл is correct.

Yes, часы is formally a plural noun, but in Russian it can mean:

• clock
• watch
• wristwatch

Context tells you which one is meant.

In this sentence, забыл часы means forgot his watch.

This is a common feature of Russian: some nouns are grammatically plural even when English uses a singular word.

Related forms:

• час = an hour
• часы = clock/watch

If you want to be more specific, you can say:

• наручные часы = wristwatch

Russian often omits possessive words like my, your, his, etc. when ownership is obvious from context.

So:

• забыл часы naturally means forgot my watch here
• saying забыл свои часы is possible, but it adds emphasis or specificity

This is very common with personal belongings and body parts:

• Я помыл руки = I washed my hands
• Он надел пальто = He put on his coat
• Я забыл часы = I forgot my watch

Russian prefers not to repeat possession when it is already clear.

Yes. Russian word order is flexible, though some versions sound more neutral than others.

The original sentence is a very natural neutral version:

• Перед работой я быстро побрился новой бритвой, а потом понял, что забыл часы.

But you could also say things like:

• Я перед работой быстро побрился новой бритвой, а потом понял, что забыл часы.
• Перед работой я новой бритвой быстро побрился...
• Часы я потом понял, что забыл — this is much more marked and stylistically different

Russian changes word order mainly for emphasis, rhythm, or information structure, not because the basic meaning changes completely. The original order is probably the best one for a learner to use.