В сумке у папы лежит бритва, потому что он иногда бреется даже в дороге.

В сумке means in the bag. After в when you are talking about location (not movement), Russian uses the prepositional case.

• сумка = bag
• в сумке = in the bag

Compare:

• в сумке = in the bag (location)
• в сумку = into the bag (motion, accusative)

So here сумке is prepositional singular.

Russian very often expresses possession with у + genitive, especially in everyday speech.

So:

• у папы literally means at dad or by dad
• in context, it means something like dad has / belonging to dad

In В сумке у папы лежит бритва, the idea is In dad’s bag, there is a razor.

You could also see an adjective like папина сумка = dad’s bag, but в сумке у папы is a very natural possessive structure in Russian.

Also note:

• папа is nominative
• у папы is genitive after у

Russian often prefers a more specific verb than to be when talking about where something is.

• лежать = to lie, to be lying
• стоять = to stand
• висеть = to hang

A razor is thought of as an object lying inside the bag, so Russian naturally says лежит бритва.

So this sounds more natural than a literal there is structure.

• В сумке лежит бритва = There is a razor in the bag / A razor is lying in the bag

Because бритва is the subject of the verb лежит.

In the clause:

• лежит = lies / is lying
• бритва = razor

The thing that is lying there is бритва, so it stays in the nominative singular.

Russian word order is flexible, and it often changes the focus rather than the basic meaning.

These are both possible:

• В сумке у папы лежит бритва
• Бритва лежит в сумке у папы

The version in your sentence starts with the location, so it feels a bit like:

• As for dad’s bag, there’s a razor in it
• or In dad’s bag, there is a razor

Russian often puts known/background information first and new/focused information later.

Because потому что introduces a subordinate clause meaning because.

Russian normally places a comma before потому что:

• В сумке у папы лежит бритва, потому что он иногда бреется даже в дороге.

This is standard punctuation.

Yes, basically.

• брить = to shave something / to shave someone
• бриться = to shave oneself, to shave

So:

• Он бреется = He shaves / He is shaving

In Russian, grooming actions are often expressed with reflexive verbs, where English just uses a normal verb:

• мыться = to wash oneself
• одеваться = to get dressed
• бриться = to shave

The ending -ся marks the reflexive form.

Russian often drops subject pronouns when they are clear from the verb form. So иногда бреется could sometimes be understood from context.

But here он is useful because it clearly links the second clause back to папа:

• ...потому что он иногда бреется... = because he sometimes shaves...

Including он makes the sentence smoother and clearer.

Даже means even.

Here it emphasizes that he shaves even while traveling / even on the road, which may be surprising or noteworthy.

• даже в дороге = even while traveling

Its position matters. It usually comes right before the word or phrase it emphasizes. Here it emphasizes в дороге.

В дороге is an idiomatic expression meaning:

• on the road
• while traveling
• during a journey

It does not usually mean physically standing on a road.

Compare:

• в дороге = while traveling
• на дороге = on the road surface / on a road

So in this sentence, даже в дороге means even when he is traveling.

Дороге is in the prepositional case because it follows в in a location/state expression.

Base form:

• дорога = road

Form here:

• в дороге = on the road / in transit / while traveling

This is another example of в + prepositional for location or state.

Иногда means sometimes.

In your sentence:

• он иногда бреется = he sometimes shaves

Russian adverbs like иногда are fairly mobile, though some positions sound more natural than others. For example:

• Он иногда бреется
• Иногда он бреется

Both are possible. The version in your sentence is very natural.

Usually бритва means razor. It can refer to a shaving razor in general.

Depending on context, Russian can also use more specific phrases, for example:

• электробритва = electric razor
• бритвенный станок = razor handle / cartridge razor / safety razor, depending on context

So бритва is a good general word here.

Grammatically, папы could come from either:

• папа = dad
• Папа = Pope

But in this sentence the meaning is clearly dad’s, because of the everyday context:

• В сумке у папы лежит бритва... = There is a razor in dad’s bag...

If it meant the Pope, the context would normally make that obvious, and Папа would usually be capitalized when written in that sense.

Because the subject бритва is singular.

• бритва = singular feminine noun
• лежит = 3rd person singular

If the subject were plural, the verb would be plural too:

• В сумке лежат вещи. = There are things in the bag.

So лежит бритва is singular because there is one razor.