Amicus tonsuram in speculo videt.

Because Latin shows grammatical function mainly through case endings, not just word order.

• amicus is nominative singular, which is the normal case for the subject
• tonsuram is accusative singular, which is the normal case for the direct object

So the endings tell you that the friend is doing the seeing, and the tonsure/haircut is what is being seen.

Here are the noun forms:

• amicus — nominative singular
• tonsuram — accusative singular
• speculo — ablative singular

Why those cases?

• amicus is the subject
• tonsuram is the thing seen
• in speculo is a prepositional phrase, and here in takes the ablative

Because it is the direct object of videt.

With a verb like to see, Latin normally puts the thing being seen into the accusative case. So:

• videt = sees
• tonsuram = the thing seen

That is a very common pattern in Latin.

Because Latin uses in with two different cases depending on the meaning:

• in + ablative = in / on in the sense of location
• in + accusative = into / onto in the sense of motion toward

Here there is no movement into the mirror. The phrase tells you where the image is seen, so Latin uses the ablative:

• in speculo = in the mirror

If it were motion into something, then you would expect the accusative instead.

Videt is:

• 3rd person singular
• present tense
• active voice
• indicative mood

It comes from video, videre.

The ending -t is the key sign of 3rd person singular, so videt means he/she/it sees.

Because Latin often does not need an explicit subject pronoun.

The verb ending already tells you the person and number:

• video = I see
• vides = you see
• videt = he/she/it sees

So videt already contains the idea of he/she sees. The noun amicus is still there to identify who that subject is.

Classical Latin has no articles.

So a noun like amicus can mean:

• a friend
• the friend

and tonsuram can mean:

• a tonsure / haircut
• the tonsure / haircut

The context tells you which English article makes the most sense.

Yes. Latin word order is much more flexible than English word order because the endings carry so much of the grammar.

For example, these could still express the same basic idea:

• Amicus tonsuram in speculo videt.
• Amicus in speculo tonsuram videt.
• Tonsuram amicus in speculo videt.
• In speculo amicus tonsuram videt.

The basic roles stay clear because of the cases. What changes is usually emphasis or style, not the core meaning.

Also, putting the verb at the end, as in this sentence, is a very common Latin pattern.

No. In a sentence like this, in speculo is understood idiomatically as in the mirror in the sense of in the reflection.

So the phrase tells you where the thing is being seen, not that anyone is physically located inside the mirror.

Yes. Amicus is a masculine singular noun.

So in ordinary usage it means a male friend or the male friend. If you wanted a feminine form, you would normally use amica.

This is worth noticing because English friend is not marked for gender, but Latin often is.

You would normally look them up like this:

• amicus, amici — masculine noun
• tonsura, tonsurae — feminine noun
• speculum, speculi — neuter noun
• video, videre, vidi, visum — verb

Those dictionary forms help you identify the declension or conjugation and understand why the sentence uses the forms amicus, tonsuram, speculo, and videt.