Mi familia siempre me apoya cuando quiero probar algo nuevo, y eso me motiva mucho.

Because familia is a singular collective noun in Spanish. Even though a family contains several people, grammatically it is usually treated as one unit.

• Mi familia siempre me apoya = singular
• If you wanted to focus on the individual members, you could say Los miembros de mi familia siempre me apoyan

This is the normal choice in Spanish.

Here me means me as the person receiving the support.

The verb pattern is apoyar a alguien = to support someone.

So:

• Mi familia apoya a Juan
• Mi familia me apoya

When you replace the full person with a pronoun, Spanish uses the object pronoun me.

This is a very common false-friend issue.

• apoyar = to support
• soportar = to tolerate, put up with, endure

So Mi familia siempre me apoya means they support me emotionally or personally.

If you said Mi familia siempre me soporta, it would sound more like My family always puts up with me, which is a very different meaning.

Because Spanish often drops subject pronouns when the verb ending already shows who the subject is.

• quiero already means I want

So cuando quiero probar algo nuevo naturally means when I want to try something new.

You could add yo for emphasis or contrast:

• cuando yo quiero probar algo nuevo

But in a normal sentence, it is usually omitted.

Because cuando without an accent is used in statements like when.

• Mi familia me apoya cuando quiero probar algo nuevo

With an accent, cuándo is used in questions or indirect questions:

• ¿Cuándo quieres probar algo nuevo?
• No sé cuándo quiere probar algo nuevo

So here, no accent is correct.

Because this sentence describes a habitual or repeated situation in the present:

• Whenever I want to try something new, my family supports me

In that kind of meaning, Spanish uses the indicative:

• cuando quiero

You would use the subjunctive after cuando if you were talking about a future or not-yet-real situation:

• Mi familia me apoyará cuando quiera probar algo nuevo

So in your sentence, quiero is the natural choice.

Probar can mean several things depending on context:

• to taste
• to try on
• to test
• to try out

Here, probar algo nuevo means to try something new in the sense of experiencing or testing it.

That is very natural Spanish.

A related verb is intentar, but it is slightly different:

• probar algo nuevo = try something new, give it a go
• intentar hacer algo nuevo = attempt to do something new

So probar fits this sentence very well.

Because with words like algo, nada, and alguien, the descriptive word normally comes after.

So you get:

• algo nuevo
• algo interesante
• nada raro

Nuevo algo is not normal Spanish.

Eso refers to the whole previous idea: the fact that the speaker’s family always supports them when they want to try something new.

So:

• y eso me motiva mucho

means:

• and that motivates me a lot

It does not refer to just one word like familia. It refers to the whole situation.

Yes, here me again means me, the person affected by the verb.

The pattern is:

• motivar a alguien = to motivate someone

Examples:

• Eso motiva a Marta
• Eso la motiva
• Eso me motiva

A useful detail: with me, you cannot tell from the form alone whether it is direct or indirect, because me can be both. But with motivar, it works like a direct-object pattern:

• Eso la motiva
• not Eso le motiva in standard usage for this meaning

Because mucho can work as an adverb with verbs and means a lot or very much.

• me motiva mucho = it motivates me a lot

But muy is used with adjectives or adverbs, not directly with verbs:

• Es muy motivador
• Habla muy rápido

So after motiva, mucho is correct.

Yes, Spanish adverbs like siempre can move around somewhat, but some positions sound more natural than others.

The most neutral order here is:

• Mi familia siempre me apoya

You could also say:

• Mi familia me apoya siempre

That is still correct, but it sounds a bit more marked or emphatic. The version in your sentence is the most natural everyday order.

In Spanish, a comma before y is usually not used, but it can appear if the writer wants a clearer pause or if the second part comments on the whole first part.

Here:

• Mi familia siempre me apoya cuando quiero probar algo nuevo, y eso me motiva mucho.

the second clause, y eso me motiva mucho, feels a bit like an added conclusion or comment.

So the comma is acceptable. That said, many people would also write this sentence without the comma:

• Mi familia siempre me apoya cuando quiero probar algo nuevo y eso me motiva mucho.

Both can be seen, though the version with the comma makes the structure a little clearer.