Yes, ALL Orthodox synagogues do, but in the other synagogues, some non-Orthodox Jews will wear their own.
Yes. Non Jews, when they attend Jewish events such as bar mitzvahs, weddings and funerals routinely wear a kippah. It is considered polite. Synagogues usually have a box of kippot (the correct plural), and sometimes, particularly at bar mitzvahs and weddings, guests are welcome to keep the kippot.
Some synagogues do, but some don't.
You can buy them at Jewish bookstores in cities that have a Jewish community. Alternatively, there are many sites online that sell kippot. Just do a search for 'yarmulkes' in a search engine such as Google and you'll find lots of place to purchase them online.
It's mostly the Orthodox Jews that do that.
Kippah is singular, while kippot is plural.
They can wear FEMININE kippot, which are made with pearls, tassels, lace, and yarn.
Some kippot stay on because of their size. Others are held on with small clips.
No, Jewish baby boys don't wear kippot. Jewish boys don't normally start wearing kippot until they're old enough to keep them on, around 2 or 3 years old.
Kippot, tallit, tzitzit
Tallitot are biblical, kippot aren't.
It is pronounced as "kee-pote" with the emphasis on the first syllable.
Kippot are the scull caps worn by religiously observant Jewish every day and other Jewish men at synagogue and while reciting prayers. There is no additional association between wearing a kippah and the holiday of Channukah.