The malonate enolate is a much stronger base than the carbonyl carbon. Adding acid will just irreversibly protonate the enolate.

Right. So the Gabriel would form a C-N bond, and then hydrolysis would lead to decarboxylation.
So ester –> carboxylic acid, and depending on choice of conditions (usually hydrazine) phthalimide —> amine.

The longest carbon chain needs to be 5 carbons, and the “core” of malonic acid will only have 2 after decarboxylation, so you need to add 3 carbons (propyl) and also an ethyl group (2-ethyl) to complete the molecule.
Starting with malonic ester, first, alkylate with propyl bromide, then ethyl bromide, then hydrolyze and decarboxylate. The result is 2-ethylpentanoic acid.

It has to do with how many C-H bonds on the central carbon of diethyl malonate have been replaced by C-C bonds. If one C-H has been replaced (e.g. with ethyl) that’s monosubstituted. If two have been replaced (e.g. with ethyl and 2-pentyl) that’s disubstituted ethyl.

If it’s an alpha, beta unsaturated beta-keto ester, yes. of course, they are great substrates.

If you’re talking about just a beta keto ester… then perhaps you are aware that they exist in the enol form. It’s possible to do addition-elimination reactions if you convert the OH to O-Tf for example and add a good nucleophile (e.g. a dialkylcuprate) but now we are getting far beyond the scope of what’s generally covered in introductory organic chem.