Temporarily you can lay a thin bead of caulking it will come off both the fridge and counter cleanly. Not seeing the issue and possible space it's difficult to advise you further. Possible to take a picture?

Hi. I hope the counter is thick enough to take the weight of the sink and water. atleast 25mm to drill in the undermount sink clips. Drill clips are available easy, you can look up Blanco and Franke EL undermount clips. If the counter is thin, you risk cracking while drilling, in which case it is better to use epoxy sink clips. A brand you can find in India is Solartime. They are expensive but you can get your local fabricator to make you a dozen clips and get them galvanised to prevent rusting. Do remember to apply silicone sealant between the undermount sink and the quartz generously. I know how you feel, things that are easily done in the west can be a pain to achieve in our country, especially places other than major cities.

Shilpa, No off the shelf products are available for this ask. You would need a creative engineer and DIY skills for this. You would need to add a compressor to make sure water reaches new faucet. Thanks, Nitin Cornerstone Designs, Bangalore.

quartz corean white synthetic marble any one as per your budget