Can I use a ceramic sink to grow cucumbers?

Why not? You would need to add some sort of drainage.

https://thriftyrebelvintage.com/2015/06/sink-planter.html/

Cucumbers need at least 8 hours of direct sunlight best to grow in a grow bag some can be grown indoors some outdoors the sink would be ideal for use of potting up seedlings

I think you’ve got drainage, and put in the right location, when they grow you can put dowels down the faucet holes for them to climb on! 🥒

Yes, you can but you need to drill a small hoe in each of the baskets to remove any excess water. Drill the hole about 2 inches up from the side and the base will act like a reservour and the plants will not dry out so quickly or rot out due to too much water.

When you do get them never put them in a fridge they are water based and lose there flavour have them in a bowl with one of those food umbrella covers over

Cucumber is a fruit

You will want to drill some holes for drainage. Maybe you could also attach some posts to lift it off the ground.

Not a good idea to use your sink as there are no drain holes in the bottom.

Go for it. Cute idea.

I know you probably already have this going but for future reference you don’t have to drill holes. I get a $3 bag of river rock for projects like this so if you get a lot of rain or over water it prevents the excess from flooding the soil. I would build a small trellis shaped like an A and push it into the soil on each side. Cucumbers love to climb and the fruit is better if it’s not laying on the soil.