Regardez is 2nd person plural, so only used if you're talking to more than one person. Regardes would be the correct 2nd person singular form if you weren't using the imperative (for example, if you were just stating a fact, "tu regardes les filles". But -er verbs loose that final s in the imperative form.
"-er" verbs lose that final "s" in the imperative form.
"Regardez" also works in the imperative (If someone were talking to more than one friend, it wouldn't say "mon ami" as Meg_in_Quebec is correct below. Click on Impératif.) http://www.larousse.fr/conjugaison/francais/regarder/7653
This is true in most cases. However, (I think) if you were saying "Look at some of them," you would write "Regardes-en" in which you would keep the s because the en starts with a vowel and is part of the same "word." So even though you would say "Regarde une fille" because "regarde" and "une" are not hyphenated, you would have to say "Regardes-en" because they have to be hyphenated. Therefore, you have to keep the s. So all this is to say that yes, the s is usually dropped in the imperative form, but not always.
To look after/keep children/anything would simply be "garder" or "s'occuper". To watch out for, as stated, is like "sauvegarder", literally to safeguard or save, and has more of a protective connotation and wouldn't be used when asking someone to watch your kids I believe, unless you were entreating them to help your children escape disaster.
Unless "watch out for" is for the second question, which would have the meaning of "beware of". Then that would be "prendre garde" or "faire attention à" http://dictionary.reverso.net/english-french/beware%20of%20being%20deceived
The infinitive of "voyez" is "voir" whose primary meaning is "to see". http://dictionnaire.reverso.net/francais-anglais/regarder http://dictionnaire.reverso.net/francais-anglais/voir
Aw, Beatriz. That is sad that you're uncomfortable. Try this. Imagine that you helped your friend make costumes for a special performance at the end of the year of private girls school. At then end of the performance the girls are all out on stage looking really cute. Your friend is distracted by her cell phone. So you nudge her and say, "look at the girls, my friend!"
That depends -- «regarder» mostly just means "look at" without any subtext. Regarde les canards (look at the ducks), regarde les enfants (look at the children), regarde les voitures (look at the cars).
We have no explicit context here, so it's probably best not to read too much into it. Whatever works best to remember it for yourself is good, of course. I think "check out" is a valid interpretation, just not "better".