You may send a gift, but it's not obligatory.
You're not required to send a gift, but usually you'll want to, unless you don't know the bride or groom well or haven't seen the couple or their families in years.
Don't do it. Enclosing gift registry cards with wedding invitations is a new phenomenon — and an inappropriate one. The guideline still stands that it's in poor taste to mention gifts in wedding invitations. Use word of mouth to get the message out about the stores where the couple has registered.
Customs vary among religions, ethnic groups, and localities. In some cases gifts are brought to the reception; more typically, they're mailed (or delivered by the store where purchased) to the newlyweds.
Thank-you notes should be written as soon as possible, within three months after the date of the wedding.
A gift check is usually written to both bride and groom unless they prefer it be made out to just one of them.
No. The amount spent on a gift should be based on the guest's affection for the couple and their families as well as the guest's financial situation.
No. The bride should thank her guests for the check without mentioning the amounts. It is appropriate, however, for the bride to mention the amount, as well as how it may be used, in the thank-you note.
Since you care about this friend, I think it would be fine to send her a gift now. (Of course, presents are preferably sent before the wedding or shortly thereafter.) I suggest you include a note saying you're sorry for the delay but you wanted her to have the gift, and offer your best wishes.
Yes to both questions. She should return gifts, with the exception of monogrammed ones, as soon as possible. If her wedding plans included a huge guest list, two months isn't an overly long time— but she shouldn't take longer than a few months.