После душа я наношу крем на руки.

Because после always takes the genitive case. The noun душ is masculine singular, and its genitive singular form is душа.

So:

• душ = shower
• после душа = after a shower / after showering

No. Here душа is the genitive singular form of душ meaning shower.

Russian also has a separate noun душа meaning soul, so the spelling is the same, but the grammar and context make the meaning clear here.

It can, but Russian often prefers a shorter noun phrase here.

• После душа... = After a shower / after showering...
• После того, как я принял душ... = After I took a shower...

Both are correct. После душа is simply more compact and very natural in everyday Russian.

Наношу is the 1st person singular present-tense form of наносить, meaning to apply.

So:

• наносить = to apply
• я наношу = I apply / I am applying

It can describe either a general habit or an action happening now, depending on context.

Because this verb changes its stem in the я form.

• наносить → я наношу

This kind of change is normal in Russian. Compare:

• просить → прошу
• носить → ношу

So наношу is the correct form.

Because the sentence describes a routine or habit: after showering, this is what I do.

Russian normally uses the imperfective for repeated, habitual, or ongoing actions.

• наносить = imperfective
• нанести = perfective

If you used the perfective, it would point more to a single completed action or to the future:

• я нанесу = I will apply

Because крем is the direct object of the verb, so it is in the accusative case.

For an inanimate masculine singular noun like крем, the accusative form is the same as the nominative form.

So:

• nominative: крем
• accusative: крем

That is why Russian says наношу крем.

Here руки is accusative plural of рука.

Russian commonly uses наносить что? на что? for applying something onto a surface or area:

• наносить крем на руки
• наносить крем на лицо
• наносить крем на кожу

So на руки means onto the hands.

Because на руки and на руках do different jobs.

• на руки = onto the hands; it shows where the cream is being put
• на руках = on the hands; it describes location or state

So in this sentence, where the action is putting/applying the cream, на руки is the right choice.

Russian often leaves out possessive words like my with body parts when the meaning is obvious.

Since the subject is я, на руки naturally means on my hands.

You can say на мои руки, but it sounds more emphatic, as if you are specifically contrasting my hands with someone else’s.

No. The given order is natural and neutral:

• После душа я наношу крем на руки.

But Russian word order is flexible, and changing it changes emphasis more than basic meaning. For example:

• Я после душа наношу крем на руки.
• Крем на руки я наношу после душа.

All of these can work, but the original version is a very normal default sentence.

Yes. That is also natural Russian.

The difference is mostly in structure and style:

• наношу крем на руки = I apply cream to my hands
• мажу руки кремом = I put/spread cream on my hands

A useful pattern difference is:

• наносить что? на что? → крем на руки
• мазать что? чем? → руки кремом

Наносить can sound a bit more neutral or skincare-related, while мазать is often more everyday and colloquial.