Vyplnil jsem formulář a podepsal ho.

No. Vyplnil is one verb form, from the verb vyplnit meaning to fill out / complete.

It only starts with a capital V because it is the first word in the sentence. It is not the formal pronoun Vy.

So:

• Vyplnil = filled out / completed
• Vy = you (formal or plural)

They just happen to look similar at the beginning.

Czech often leaves out subject pronouns when they are clear from the verb.

Here, jsem tells you this is first person singular: I.

So:

• Vyplnil jsem formulář = I filled out the form

You could add já:

• Já jsem vyplnil formulář

But that usually adds emphasis, contrast, or clarity. In normal neutral sentences, Czech often omits já.

Because jsem is a short unstressed word, called a clitic, and Czech usually places clitics in second position in the clause.

So in:

• Vyplnil jsem formulář

the first element is Vyplnil, and jsem comes right after it.

This word order is very normal in Czech past tense.

You can also get:

• Já jsem vyplnil formulář

because já is then the first element, and jsem goes after it.

Because Czech often uses the auxiliary only once when two past-tense verbs share the same subject.

So:

• Vyplnil jsem formulář a podepsal ho

means:

• I filled out the form and signed it

The jsem belongs with both verbs.

You could also say:

• Vyplnil jsem formulář a podepsal jsem ho

That is also grammatical, but the version with only one jsem is very natural and common.

That -l is part of the Czech past-tense form.

In this sentence, the speaker is masculine singular, so you get:

• vyplnil
• podepsal

If the speaker were female, it would be:

• Vyplnila jsem formulář a podepsala ho.

If the subject were plural, the forms would change again.

So the ending helps show gender and number in the past tense.

Here formulář is the direct object, so it is in the accusative case.

But formulář is a masculine inanimate noun, and for many nouns of that type, the nominative singular and accusative singular look the same.

So:

• nominative: formulář
• accusative: formulář

That is why the form does not change.

Compare that with a masculine animate noun, where the accusative usually looks different:

• student → studenta

Ho means him/it here, and it refers back to formulář.

Because formulář is a masculine singular noun, the matching accusative pronoun is:

• ho
  or
• jej (more formal/full-sounding)

In everyday Czech, ho is very common.

So:

• podepsal ho = signed it

Because to is used mainly for neuter nouns or for this/that/it in other kinds of structures.

But formulář is masculine inanimate singular, so the normal object pronoun is:

• ho or
• jej

So after formulář, Czech naturally says:

• podepsal ho

not podepsal to

Again, this is because ho is a short unstressed pronoun, a clitic.

In Czech, clitics tend to appear near the beginning of their clause, usually in second position.

In the second part of the sentence:

• a podepsal ho

the clause after a begins with podepsal, so ho follows it.

If you included jsem again, you would normally say:

• a podepsal jsem ho

with the short words placed early in the clause.

Because Czech does not have articles like English a/an/the.

So:

• formulář can mean a form or the form

The exact meaning depends on context.

That is completely normal in Czech. Learners often want to add an article, but Czech simply does not use one.

Yes. Both are perfective, which means they present the actions as completed.

• vyplnit = to fill out completely / finish filling out
• podepsat = to sign

That fits the sentence well, because it describes two finished steps:

1. I filled out the form.
2. I signed it.

If you wanted to focus on the process instead, you would use imperfective forms, for example:

• Vyplňoval jsem formulář a podepisoval ho.

That sounds more like I was filling out the form and signing it or describes the action as ongoing/repeated rather than simply completed.

You usually use ho because it sounds natural and avoids unnecessary repetition.

Natural:

• Vyplnil jsem formulář a podepsal ho.

Less natural if there is no special reason:

• Vyplnil jsem formulář a podepsal formulář.

You can omit the object in some contexts if it is obvious, but in a standalone sentence Czech normally keeps ho:

• Vyplnil jsem formulář a podepsal.
  This can sound incomplete unless the context already makes the object very clear.

So ho is the normal choice here.

The stress in Czech is normally on the first syllable, so:

• FOR-mu-lář

A few useful points:

• á is a long vowel
• ř is a special Czech sound with no exact English equivalent

A rough learner-friendly approximation might sound like:

• FOR-moo-laarzh

That is not perfect Czech pronunciation, but it can help as a first step.