Στο πλυντήριο βάζω απορρυπαντικό και μαλακτικό, αλλά όχι πολύ.

Στο is a contraction of σε + το (in/into + the).
So Στο πλυντήριο literally means in/into the washing machine (or sometimes at the laundry/washer, depending on context). Greek commonly contracts:

• σε + το → στο
• σε + τη(ν) → στη(ν)
• σε + τα → στα

πλυντήριο is the common word for washing machine. It can also refer to a laundry place in some contexts, but in a household sentence like this it almost always means the machine.
πλύσιμο means washing as an activity/process (e.g., Το πλύσιμο των ρούχων = washing clothes), not the machine.

βάζω literally means to put / to place, and it’s very natural in Greek for “adding” things to a machine or container.
In this context it corresponds to I put/add detergent and fabric softener.

Greek present tense often covers:

• habitual/general actions: When I do laundry, I put…
• instructions/routine narration: First I put…, then… So here βάζω can mean I (usually) put.

Greek often drops subject pronouns because the verb ending shows the person.
βάζω already means I put (1st person singular), so εγώ (I) is unnecessary unless you want emphasis/contrast.

Both are possible:

• Without article (βάζω απορρυπαντικό και μαλακτικό) sounds like some detergent and (some) softener—a general, uncountable “substance” sense.
• With articles (βάζω το απορρυπαντικό και το μαλακτικό) can sound more specific, like the detergent (we use) and the softener (we use), or talking about those particular products.

They are neuter nouns here:

• (το) απορρυπαντικό = detergent
• (το) μαλακτικό = fabric softener
  They come from adjectives/derived forms, but in everyday Greek they function as standard product nouns.

By default, αλλά όχι πολύ usually applies to the whole previous idea: I put detergent and softener, but not much (i.e., not too much overall).
If you wanted to clearly limit it to just one, you might specify:

• …και μαλακτικό, αλλά όχι πολύ μαλακτικό. = but not much softener.

δεν negates verbs:

• Δεν βάζω πολύ. = I don’t put much.

όχι is used for short/contrastive negation like no / not and often follows αλλά:

• …αλλά όχι πολύ. = …but not much.

Both can be correct depending on style, but αλλά όχι πολύ is very idiomatic.

Yes. Greek word order is flexible. Common alternatives include:

• Στο πλυντήριο βάζω απορρυπαντικό και μαλακτικό… (sets the scene first: In the washing machine…)
• Βάζω απορρυπαντικό και μαλακτικό στο πλυντήριο… (focuses first on what you add)
• Βάζω στο πλυντήριο απορρυπαντικό και μαλακτικό… (very neutral)

The meaning stays basically the same; the fronted phrase often gives it extra emphasis.