You do not need to present a birth certificate to use a passport for its intended purpose. A passport alone is sufficient proof of nationality/citizenship. You may need to present a birth certificate in order to apply for a passport.
Yes, a certificate of live birth can be used as a primary form of identification when applying for a passport.
No you need a passport
No
With the U.S.'s new restrictions, you need a passport any time you leave the country. You'll want the birth certificate to get the passport, though, so in a sense you do use it to go on a cruise.
No you need a passport.
No.
No
Yes, a laminated birth certificate can be used to obtain a passport as long as it is in good condition and all information is clearly visible and legible.
In most countries, yes you can.
No you will need a visa. To get that you will need a passport. To get a passport your country will normally require that you present you birth certificate. Citizens of some countries may not actually have to have a visa, if their home country participates in the Visa Waiver Program. You can check with the nearest US Embassy or Consulate to see if you need a visa or not; you'll definitely need the passport, though.
birth certificate
Only within the US. You'll need a passport to leave the country, even to go to Canada.