"Mögen" is used for "Wir". "Mag" is used for "Ich".
Wir mögen. Ich mag.
In german, each verb has a different form for each pronoun. Next time, when you see the german word in your exercises, click it and from the drop down click "conjugate". Or just google it, or find the word in the "words" tab up there and click conjugate :D
Usually yes. But, if what you misspelled becomes another word or is unrecognisable to Duo, it will mark you wrong.
For example, a single letter mistake can make you wrong: "Wir mögen Restaurants"(We like restaurants), to "Wer mögen Restaurants" (Who like restaurants).
This changes the concept of the sentence AND makes it grammatically incorrect. Duolingo isn't alive & thus can't always tell whether you just made a spelling error or if you don't understand the material yet.
Try writing out the word on paper & spelling it out at the same time.
(Assuming you spelt "die Restaurant" wrong, it may help that it's spelt the same in English, French, Dutch, Danish & Norwegian among others. For each of these languages -including German- the word comes from the French who pronounce "au" as an "oh!" sound. Ultimately, restaurant came from the Latin word for "restore", restaurāre).