Lavabo, lavello and lavandino all work for both a bathroom and a kitchen sink/basin (usage varies regionally); "vasca" is normally used for bigger containers, from a bathtub to a swimming pool, while "vaschetta" is used for smaller containers, and normally movable ones (vaschetta di gelato, a bowl of ice cream).
The verb riempire is interesting, at least for those who speak French, as one might guess that must be conjugated as riempisco, riempisci, riempisce, riempiamo, riempiate, riempiscono. And indeed it can be, though native speakers might tell us which is preferred. In French, it's je remplis, tu remplis, il/elle remplit, nous remplissons, vous remplissez, ils/elles remplissent.
It's not idiomatic. When we 'fill in' we are suggesting that for something to be 'complete' - as it should be - something that is lacking needs to be put in it.
You can fill a bottle or leave it empty. It doesn't matter. But if you are given an insurance form, for example, and there are blank spaces for your name, age, etc., then the whole purpose of the form is for all the blanks to be filled in - no gaps, nothing missing. The form is 'complete' when it is filled in (in UK English; in the US, they 'fill out' forms)- when something is IN every blank on the form.
Suppose you have to be absent from work. Normally, properly, you would be at work, 'filling' your position in your place of business. But you have to be absent. Now there's a 'gap' where you would normally, properly be. So you ask your cousin to 'fill in' for you. He 'fills the space' created by your absence.
Try to think of it as an absence, a gap, a space with nothing IN it when something should be IN it. Then you're more likely to use 'fill in' rather than just 'fill.'
You have to be careful, though, if you are not a native-speaker, because we have other phrasal verbs with 'fill' that work idiomatically: fill UP (up to the top of, say, the bathtub or a glass); fill OUT (a form, in US English; also we say that when a girl's body develops into a woman's body, she 'has filled out' and that now she can 'fill out' a sweater, for example).
Phrasal verbs are very hard to explain. You just have to get a feel for them over time. If you wonder about a verb like 'fill in,' and how to use it, try searching Google books (not just webpages) in English for exactly that phrase, and reading the verb used in many contexts. Eventually you'll get a sense of when it is used naturally.