A U.S. patent gives the holder the right to exclude others from “practicing” the claimed inventions in the United States. “Practicing” means making, using, selling, importing, or exporting. If you want patent coverage in a foreign country you need to secure a patent in that foreign country. Sometimes people mistakenly think that getting a patent means they have a right to do what the patent claims. That’s completely wrong. A patent only give a right to stop other from doing what a claim says.
A patent gives the holder the right to exclude others from “practicing” the claims set forth in an issued patent (unless of course that patent is expired or invalidated). Claims are read literally. If a claim recites a vehicle with two wheels, then a vehicle with three wheels falls outside the scope of the claims. If the claim recites a vehicle with first and second wheels, then a vehicle with three wheels falls inside the scope of the claims because even though it has a third wheel, it does have first and second wheels. Very often a claim uses terms that have multiple possible meanings, and for those terms one needs to review the specification, drawing, abstract, other claims, history of arguments during prosecution, and even prosecution history of family patents. Even then the meaning of a claim term may need to be decided by a court, possibly using expert witnesses and other extrinsic information.
In a technical sense, the answer is “no.” The scopes of the claims in the different patents necessarily differ from one another, so they are not directed to the “same invention.” In a practical sense, the answer is “yes. ” Applicants often file multiple applications on different aspects of an invention. Those applications can proceed in parallel, or they can be prosecuted sequentially. In addition, the patent office regularly issues “restriction requirements” on applications filed with multiple independent claims. In that case the applicant either needs to drop the excess claims, or prosecute them in one or more separate applications. Still further, many applicants file a divisional or continuation after the patent issues, just so they can keep something pending.
Generally not. Patents are almost entirely national, so that a patent in the U.S. will not protect you against manufacture, sale or us in a foreign country. However, it is illegal to import a product that is patented in the U.S., or a product made using a patented method, into the U.S. There is also some case law under which U.S. district courts can exert their authority over actions taken in foreign countries; the so-called extra-territorial enforcement of U.S. patent rights. Eolas v Microsoft, 399 F. 3rd 1325 (Fed. Cir. 2005); AT&T v Microsoft, 414 F, 3d 1366 (Fed. Cir. 2005); Union Carbide v Shell, 425 F.3d 1366 (Fed. Cir. 2005). There is a good analysis in Strategic Patenting.