Alien life may not be carbon-based, new study suggests

1. You can eat them if they have the nutrients you need. Non-carbon-based just means it won't use carbon as the foundation of its molecular and cellular workings. By mass, there's relatively little carbon in living organisms and on earth, so whatever's out there could still use carbon and other elements enough that it has something we could eat. There's barely any telling what kinds of chemicals will be found in an organism like that, but it could easily be a mix of things we can digest and things we can't. Even carbon-based life is like that. Wood for example is biologically very similar to us, but is mainly made of cellulose, which we can't really digest at all.
2. yes, if it fits.

God I hope it's slime girls

Both of those questions will depend on what kind of environment they need to survive. They might need pressures higher than we can or a pH that would be corrosive to us, or exposure to an chemical that is toxic to us like oxygen was to most life that was around when photosynthesis started producing it.

If we can make physical contact with it, we'll be able to eat it. But if it is based on a different chemistry, I doubt there will be much nutritional value for us as our proteins and vitamins are all based on our chemistry. Hell, there's a good chance we won't get much nutrition from alien life based on the same chemistry because they might have evolved with a completely different set of proteins that might do things similarly but connect with each other a bit differently. There's a symmetrical set of proteins that look like mirror images of ours and would behave exactly the same, but aren't compatible with ours.

Is there anything we can't fuck?

Have you read Sphere?

You can go one step further: life is just an area of low entropy keeping itself like that by increasing the entropy of its environment.

We poop out randomness to keep ourselves not random.

There's good reason to presume carbon is required. Carbon has some nice, and totally unique properties that allow it to facilitate life.

The most important features to carbon in this context are:

1. Stable catenation of atoms. Carbon atoms can bond to other carbon atoms in a long chain, and that chain does not become appreciably more reactive. This allows for the construction of very large molecules with specialized mechanical functions.
2. Ability to form stable multiple bonds. Carbon can form single, double, or triple bonds with itself (and oxygen and nitrogen), which allows carbon-based molecules to have ridgid shapes. Double bonds are found all over the place in life because they allow molecules to have sections that aren't just wiggly noodles of atoms.
3. Bond stabilities that fall in a kind of "goldilocks zone" where carbon bonds to other atoms are strong enough to resist falling apart, but weak enough to be broken later.
4. Nearly identical electronegativity to hydrogen. Carbon pulls on the electrons in its bonds about the same amount as hydrogen. This allows it to make stable bonds that are non-polar, which, when used in conjuction with other, more electronegative atoms (particularly oxygen and phosphorus) allow Carbon-containing molecules to be hydrophobic, hydrophilic, or both simultaneously. This property is what allows for complex structures like Lipid bilayers and proteins to be formed.

No other atom, not even silicon, has this set of properties, and it's very hard to imagine how you would make all but the most simplistic verson of life without these.