Ver pequeños avances hace que me motive y que no me desanime tanto.

Yes. In Spanish, an infinitive can act like a noun and be the subject of a sentence.

So Ver pequeños avances means something like seeing small improvements. That whole infinitive phrase is the subject of hace.

This is very common in Spanish:

• Leer me relaja. = Reading relaxes me.
• Viajar abre la mente. = Travelling opens the mind.

You could also sometimes see El ver pequeños avances..., but the article el is often omitted.

Because the true subject is not just avances. The subject is the whole idea Ver pequeños avances.

That whole infinitive phrase is treated as a singular action or concept, so the verb is singular:

• Ver pequeños avances hace...
• Comer bien ayuda...
• Dormir poco afecta...

Even though avances is plural, it is only part of the infinitive phrase.

Here hacer que means to make, to cause, or to lead to.

So the structure is:

• [something] hace que [subjunctive clause]

In this sentence:

• Ver pequeños avances hace que...
• Seeing small improvements causes the following result.

This is a very common pattern in Spanish:

• Eso hace que me sienta mejor. = That makes me feel better.
• La lluvia hace que no salgamos. = The rain makes us not go out.

Because after hacer que, Spanish normally uses the subjunctive in the following clause.

So:

• hace que me motive
• hace que no me desanime tanto

The idea is that ver pequeños avances causes a reaction or result, and Spanish expresses that result with the subjunctive.

That is why you get:

• me motive rather than me motivo
• me desanime rather than me desanimo

This is standard grammar after hacer que.

It can look that way at first, but here it is better understood as I get motivated or I feel motivated.

Spanish often uses verbs like motivarse and desanimarse in a pronominal way:

• motivarse = to get motivated
• desanimarse = to get discouraged

So me motive means something like I become motivated, not necessarily that I actively motivate myself on purpose.

If you want a version that sounds more explicitly like feel motivated, you could say:

• Ver pequeños avances hace que me sienta motivado/a...

That may feel clearer to some learners.

Me refers to the speaker and shows that the effect happens to them.

In these pronominal uses:

• me motive = that I get motivated
• me desanime = that I get discouraged

So me is not an indirect object like in English it motivates me. Instead, it is part of the pronominal verb structure.

Compare:

• Esto me motiva. = This motivates me.
  Here motiva is a normal transitive verb.

• Esto hace que me motive. = This makes me get motivated.
  Here motivarse is being used in a pronominal way.

Because the sentence is linking two parallel subordinate clauses, both dependent on hace:

• que me motive
• que no me desanime tanto

Repeating que makes the structure clear and balanced.

You may also hear:

• Ver pequeños avances hace que me motive y no me desanime tanto.

That is also understandable and often natural. But repeating que is very common when the speaker wants to clearly show that both verbs depend on hace que.

Because tanto is used with verbs, while tan is used with adjectives and adverbs.

Here tanto modifies the verbal idea desanimarse:

• no me desanime tanto = that I do not get discouraged so much / as much

Compare:

• trabaja tanto = he works so much
• es tan difícil = it is so difficult
• habla tan rápido = she speaks so quickly

So in this sentence, tanto is the correct choice.

Yes. The original sentence is grammatical, but there are other very natural ways to say it.

For example:

• Ver pequeños avances me motiva y no me desanima tanto.
• Ver pequeños avances hace que me sienta motivado/a y que no me desanime tanto.

The first version is more direct: Seeing small improvements motivates me and doesn’t discourage me as much.

The original version with hace que is slightly more structured and explicitly expresses cause and result.

Because the main verb hace is in the present, and the sentence is talking about a general, current effect.

So the natural tense is the present subjunctive:

• hace que me motive
• hace que no me desanime tanto

If the main verb were in the past, you would normally shift the subordinate verb too:

• Ver pequeños avances hacía que me motivara y que no me desanimara tanto.

So the tense choice matches the time frame of the sentence.