Translation:This place is a cafeteria.
Kanji next to other kanji use the Chinese or onyomi reading which for 食 is しょく。Same for 夕食 (ゆうしょく)。When its by itself it uses the Japanese or kunyomi reading which is たべ。The vast majority of kanji behave like this. There are always exceptions like body parts, but you can almost always bet two kanji next to each other in a noun will sound different than when you see it alone in a verb with hiragana.
Kanji can have on-yomi and kun-yomi readings. So a Kanji can have several readings even though it has the same or similar meaning. So for 食, it can read た-べる for its kun-yomi reading or ショク as well as ジキ for its on-yomi. Usually if the Kanji is with another Kanji like this example, you use the on-yomi reading. I suggest you download an app like Kanji Study to further learn the readings and meanings.
"Koko" means "here".
Koko wa shokudo desu. [Here is the canteen.]
"Kono" means "this", but a noun is expected right after it.
E.g.: Kono kuruma wa ao desu. [This car is blue.]
In the other hand we have "kore" (this) which is used without a noun right after.
E.g.: Kore to kore wo kudasai. [(I'll have - give me) this and this please.]
No, it's because of the meaning of the sentence. です is used to equate things -- "A is B" -- while あります is used to talk about existence: "there is A", or in other words "A exists". ここ can be used with either, but in this case we are using the former because we are talking about what "this place" is (a cafeteria), not that it exists.
A similar sentence using あります would be ここにしょくどうがあります -- "here, there is a cafeteria". Note that ここは in the original is the topic, the thing ("this place") that is talked about, while ここに in the new sentence shows the place ("here") where something exists.
Dining room is the place to eat in a personal home. A dining hall is much larger and fancier, found at fancy schools, military bases, convention centers, schools of witchcraft and wizardry, and sometimes churches. It's a more formal space than a cafetería or chow hall - ie food is usually "dished" in another room, there are chandeliers instead of fluorescent tubes, and windows typically have curtains.
Errr, duolingo translates the word as "dining room" when hovered over, however when selecting from words the closest option was cafeteria. In America at least, a dining room is the room in your house where you eat. It's usually not used when referring to a cafeteria or other public eating establishments.
this website has a table for pronouns. Very useful