Marco inventa una soluzione.

In Italian, subject pronouns are often left out because the verb ending already shows who the subject is.

• invento = I invent
• inventi = you invent
• inventa = he/she invents

So Marco inventa is completely natural, and Marco already tells you who the subject is.

You could say lui inventa, but that would usually add emphasis, such as contrast:

• Marco inventa una soluzione, non Paolo.
  Marco comes up with a solution, not Paolo.

Inventa is the third person singular present tense of inventare.

That means it can mean:

• he invents
• she invents
• it invents
• and in many contexts, also is inventing or does invent, depending on English translation

With Marco, it means Marco invents / comes up with.

Yes. Inventare is a regular -are verb.

Its present tense is:

• io invento = I invent
• tu inventi = you invent
• lui/lei inventa = he/she invents
• noi inventiamo = we invent
• voi inventate = you all invent
• loro inventano = they invent

So inventa follows the normal pattern for -are verbs.

Because soluzione is a feminine singular noun, so it takes the feminine singular indefinite article una.

• un = masculine singular
• una = feminine singular

So:

• un problema
• una soluzione

Even though soluzione ends in -e, it is still feminine.

Good question. In Italian, nouns ending in -e can be either masculine or feminine, so the ending alone does not always tell you the gender.

You often have to learn the gender together with the noun:

• il problema = masculine
• la soluzione = feminine

A useful clue here is the ending -zione, which is very often feminine:

• la stazione
• la lezione
• la situazione
• la soluzione

So soluzione is feminine: una soluzione.

It can often mean both, depending on context.

In English, invent can sound like creating something totally new, while in Italian inventare can also be used more broadly for devising or coming up with something.

So Marco inventa una soluzione may mean:

• Marco invents a solution
• Marco comes up with a solution

The exact nuance depends on context.

Italian word order is more flexible than English, but not every order sounds equally natural.

The most neutral sentence is:

• Marco inventa una soluzione.

You can change the order for emphasis, but it may sound marked or literary:

• Una soluzione la inventa Marco.
  It’s Marco who comes up with a solution.

Without context, Una soluzione inventa Marco sounds unusual. So for normal use, stick with subject + verb + object here.

Because Marco is a proper name, and proper names in standard Italian usually do not take an article in this kind of sentence.

So:

• Marco inventa una soluzione.

That is normal and correct.

In some regional varieties or special contexts, personal names may appear with an article, but that is not the standard pattern you should use here.

Soluzione is pronounced roughly so-loo-TSYO-neh.

The stress is on the syllable -zio-:

• so-lu-zio-ne

That zi sound is like tsy in English approximation, not like the z in zoo.

Inventa is pronounced roughly een-VEN-ta.

The stress is on the second syllable:

• in-ven-ta

A few pronunciation notes:

• i sounds like ee in see
• e here is a clear eh sound
• a is like ah

Yes, but the meaning changes slightly.

• Marco trova una soluzione = Marco finds a solution
• Marco inventa una soluzione = Marco invents / devises / comes up with a solution

Trova focuses on finding a solution. Inventa focuses on creating or devising one.

So both can work in some situations, but they are not exactly the same.