Puse grasa en la cadena.

Because puse is the 1st person singular preterite of poner (to put), and poner is irregular in the preterite.

The pattern is:

• yo puse
• tú pusiste
• él/ella/usted puso
• nosotros pusimos
• vosotros pusisteis
• ellos/ellas/ustedes pusieron

So puse grasa means I put grease.

Spanish often leaves out subject pronouns because the verb ending already shows who the subject is.

• Puse already means I put
• So yo is not necessary

You could say Yo puse grasa en la cadena, but that usually adds emphasis, contrast, or clarity, for example:

• Yo puse grasa en la cadena, no aceite.
• I put grease on the chain, not oil.

Without emphasis, Puse grasa en la cadena is the normal way to say it.

Because grasa is being used as a mass noun, like water, oil, or sand in English.

So Puse grasa means something like:

• I put grease
• I put some grease

Spanish often omits the article with an unspecified amount of a substance.

Compare:

• Puse grasa en la cadena = I put grease / some grease on the chain
• Puse la grasa en la cadena = I put the grease on the chain

The second one sounds like you mean a specific grease already known in the conversation.

Because en can cover both in and on in many cases.

So:

• en la mesa = on the table
• en la caja = in the box
• en la pared = on the wall

Spanish does not always separate in and on the way English does. Here, en la cadena naturally means on the chain.

La cadena suggests a specific chain that is already understood from the context.

For example, if you are talking about a bike, a machine, or a door chain, Spanish often uses the definite article when the object is obvious.

• Puse grasa en la cadena = I put grease on the chain

You could also say:

• Puse grasa en una cadena = I put grease on a chain
  
  • sounds indefinite, as if the chain is not identified
• Puse grasa en mi cadena = I put grease on my chain
  
  • explicitly says it is yours

Spanish uses the definite article quite often where English might use my, your, or just leave it implied.

Yes. That is a very natural alternative.

• Puse grasa en la cadena focuses on the grease being placed on the chain
• Le puse grasa a la cadena treats the chain more like the recipient of the action

In everyday Spanish, especially with this kind of structure, le ... a la cadena is common.

A rough contrast:

• Puse grasa en la cadena = I put grease on the chain
• Le puse grasa a la cadena = I put grease on the chain / I greased the chain

Both are fine. The second one sounds a bit more like applying something to the chain.

Yes, especially in Spain.

In Spain, the present perfect is often used for recent past actions or actions connected to the present:

• He puesto grasa en la cadena = I’ve put grease on the chain

While:

• Puse grasa en la cadena = I put grease on the chain

Very roughly:

• he puesto often sounds more connected to now or today
• puse sounds more like a finished action in a past narrative

Both are correct. In Spain, he puesto is especially common if the action happened recently.

Here it normally means grease as a lubricant.

Grasa can mean:

• fat/grease in a general sense
• mechanical grease in contexts like bikes, chains, engines, and tools

If you were talking about lubricants, grasa is completely natural.

A useful contrast is:

• grasa = grease
• aceite = oil

So for a chain, both may be possible depending on the product, but grasa is fine if you specifically mean grease.

Often, yes.

Engrasar means to grease or to lubricate with grease.

So:

• Engrasé la cadena = I greased the chain

This is shorter and often more idiomatic than Puse grasa en la cadena.

Still, Puse grasa en la cadena is perfectly understandable and natural enough, especially for a learner or in plain speech. It is just a bit more literal: I put grease on the chain.

The most neutral order is:

• Puse grasa en la cadena

That is the normal, unmarked version.

You can move elements for emphasis, but it changes the feel:

• En la cadena puse grasa = On the chain, I put grease
  
  • possible, but marked for emphasis or contrast
• Grasa puse en la cadena = Grease is what I put on the chain
  
  • also possible, but strongly emphatic
• Puse en la cadena grasa
  
  • this sounds awkward in ordinary speech

So for everyday use, Puse grasa en la cadena is the best choice.

Because grasa is a feminine noun in Spanish, so it takes feminine articles and adjectives:

• la grasa
• mucha grasa
• grasa espesa

Likewise, cadena is also feminine:

• la cadena
• la cadena vieja

There is no special reason visible from this sentence alone; it is simply part of each noun’s grammatical gender and must be learned with the word.