Ich wasche mir die Hände am Waschbecken.

Because German often uses the pattern:

subject + verb + dative person + body part

So literally, Ich wasche mir die Hände means something like I wash myself the hands, but in natural English we say I wash my hands.

• mir = dative, meaning for myself / on myself
• die Hände = the thing being washed

German treats the body part as the direct object and the person as an indirect object.

Compare:

• Ich wasche mir die Hände. = I wash my hands.
• Ich wasche mich. = I wash myself. / I am washing myself.

So mich would change the meaning.

With body parts, German very often uses the definite article instead of a possessive adjective when it is already clear whose body part it is.

So:

• Ich wasche mir die Hände.

is more natural than:

• Ich wasche meine Hände.

Both are possible, but die Hände is the normal German way here because mir already shows that the hands belong to me.

English usually says my hands, but German often prefers:

• Er putzt sich die Zähne. = He brushes his teeth.
• Sie wäscht sich das Gesicht. = She washes her face.

Die Hände is in the accusative case because it is the direct object of waschen.

Here is the structure:

• Ich = subject, nominative
• wasche = verb
• mir = indirect object, dative
• die Hände = direct object, accusative

Since Hände is plural, the form die Hände looks the same in nominative and accusative. But functionally, here it is accusative.

The singular is:

• die Hand = the hand

The plural is:

• die Hände = the hands

So Hände is simply the normal plural form.

It is not Händen because that would usually be the dative plural form, for example:

• mit den Händen = with the hands / with your hands

But in your sentence, die Hände is the direct object, so it is accusative plural.

Am is a contraction of:

• an dem

So:

• am Waschbecken = at the sink / by the sink

This is very common in German:

• am Tisch = at the table
• am Fenster = by the window
• am Bahnhof = at the train station

In your sentence, am Waschbecken tells you the location where the action happens.

Because am Waschbecken means at the sink or by the sink, while im Waschbecken means in the sink.

That is an important difference:

• Ich wasche mir die Hände am Waschbecken. = I wash my hands at the sink.
• Ich wasche mir die Hände im Waschbecken. = I wash my hands in the sink.

Both can make sense, but am Waschbecken is the more usual way to describe the place where you stand to wash your hands.

Because Waschbecken is a noun, and all nouns in German are capitalized.

So:

• ich = not capitalized in the middle of a sentence
• wasche = verb, not capitalized
• mir = pronoun, not capitalized
• die Hände = noun Hände capitalized
• das Waschbecken = noun capitalized

This is one of the most noticeable spelling differences between German and English.

Grammatically, yes, but it sounds incomplete or unusual if you mean my own hands.

Without mir, the sentence sounds more like:

• I am washing the hands

That could mean someone else's hands, or hands in a more abstract sense. German normally includes mir when talking about washing your own body part:

• Ich wasche mir die Hände.

So if you mean your own hands, mir is the natural choice.

It is related to reflexive usage, but not in exactly the same way as verbs that always require a reflexive pronoun.

Here, waschen can be used in several ways:

• Ich wasche das Auto. = I wash the car.
• Ich wasche mich. = I wash myself.
• Ich wasche mir die Hände. = I wash my hands.

So waschen is not always reflexive, but when you wash a part of your own body, German often uses this dative reflexive-like construction: mir die Hände, sich die Haare, and so on.

The sentence follows a very typical German main-clause pattern:

Ich | wasche | mir | die Hände | am Waschbecken.

• Ich = subject
• wasche = conjugated verb in second position
• mir = dative object
• die Hände = accusative object
• am Waschbecken = location

German main clauses usually put the conjugated verb in position 2.

You could also change the emphasis by moving another element to the front:

• Am Waschbecken wasche ich mir die Hände.

But then the verb still stays in second position:

• Am Waschbecken | wasche | ich | mir die Hände.

Yes. The German present tense can often translate as either:

• I wash my hands at the sink
• I am washing my hands at the sink

Which English version is best depends on context.

German Ich wasche does not by itself force a distinction between simple present and present progressive the way English often does.

Not exactly.

• Waschbecken usually means a bathroom sink or washbasin.
• Spülbecken usually means a kitchen sink.

So in your sentence, am Waschbecken strongly suggests washing your hands in a bathroom or similar place.

A simple pronunciation guide is:

ikh VASH-uh meer dee HEN-duh am VASH-bek-en

A few key points:

• ich: the ch is a soft sound, not like English k or ch in church
• wasche: the sch sounds like English sh
• mir sounds roughly like meer
• Hände has an umlaut ä, somewhat like e in bed, but not exactly
• Waschbecken has stress on the first part: WASH-becken

If you want to sound natural, keep the sentence flowing smoothly rather than stressing every word equally.