Este queso no es picante, pero el café me sabe amargo.

Because picante is being treated as a normal characteristic of the cheese's flavor. For basic descriptions like this, Spanish usually uses ser.

• es picante = it is spicy
• está picante would sound less standard here and more like a temporary condition or a special circumstance

For food taste in general descriptions, ser is the safer choice.

Here picante means spicy/hot in the sense of chili heat.

In Spain, picante usually refers to food that has a sharp, hot sensation. It does not usually mean simply full of spices. So queso picante is a cheese with some heat to it, not just a well-seasoned cheese.

Yes. That is very natural.

With food, picar can mean to sting/burn a little in the mouth, so:

• Este queso no es picante = This cheese isn't spicy.
• Este queso no pica = This cheese doesn't have that spicy bite.

Both are correct. No pica sounds a bit more everyday and sensory.

Because saber means to taste, and it expresses how something tastes to someone.

• El café es amargo = The coffee is bitter.
  A general statement about the coffee.
• El café me sabe amargo = The coffee tastes bitter to me.
  A statement about your experience of it.

So saber adds the idea of personal perception.

Me means to me.

Spanish often uses an indirect object pronoun with saber when talking about taste:

• me sabe = tastes to me
• te sabe = tastes to you
• le sabe = tastes to him/her/you
• nos sabe = tastes to us

So el café me sabe amargo literally means the coffee tastes bitter to me.

Because amargo agrees with el café, which is masculine singular.

The adjective does not agree with me. The person experiencing the taste does not control adjective agreement.

Compare:

• El café me sabe amargo
• La leche me sabe amarga

The adjective matches the thing that tastes that way.

Yes. That is very common.

You can say:

• sabe dulce
• sabe salado
• sabe amargo
• sabe raro

If you name a specific flavor or thing, Spanish often uses saber a + noun:

• sabe a limón
• sabe a vainilla
• sabe a humo

So:

• sabe amargo = tastes bitter
• sabe a limón = tastes like lemon

Spanish uses articles more often than English does.

Here el café probably means:

• the coffee being served
• the coffee you are talking about
• coffee in a specific context

In English, we might often just say coffee, but Spanish frequently prefers el café when the referent is understood.

Because este means this, usually something close to the speaker or mentally close in the conversation.

• este queso = this cheese
• ese queso = that cheese

A learner often notices that Spanish keeps this distinction very clearly. If the cheese is the one in front of you, este queso is the natural choice.

Because pero joins two full clauses here, and Spanish normally puts a comma before it.

The two clauses are:

• Este queso no es picante
• el café me sabe amargo

This works much like English but in similar sentences.

Because pero introduces a contrast, while sino replaces or corrects something after a negation.

Use sino like this:

• No es queso, sino mantequilla.
  It isn't cheese, but rather butter.

In your sentence, the second part is not correcting queso. It is just adding contrasting information about the coffee. So pero is correct:

• Este queso no es picante, pero el café me sabe amargo.

A simple pronunciation guide:

• queso = KEH-so
• picante = pee-KAN-teh
• café = ka-FEH
• amargo = a-MAR-go

The accent mark in café shows that the stress falls on the last syllable: ka-FEH.