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The SFO > CDG flight is international, departing the US and arriving in France (a member of the Schengen area).
While the flight from CDG > WAW is international (between countries), it is from one Schengen state (France) to another Schengen state (Poland). Inter-Schengen flights are without systematic Immigration checks.
If you fly on separate tickets, you'll pass through Immigration and Customs at CDG. If you fly both legs on one ticket, you'll pass Immigration at CDG and Customs at WAW.
Provided you've adhered to the Schengen Visa Code about from which Schengen state you obtained your Schengen visa, you can enter the Schengen area through any of its member states. A discussion of the issue can be found here.
So the answers to your questions are:
No.
Yes, as you'll pass Schengen Immigration at CDG.
The issue is: what happens if you miss a flight? If on a single ticket, the airline is responsible to get you to your destination (here, WAW) and put you up on the way if that's necessary, and perhaps pay you compensation if the delay is significant. Because of the cost of this added responsibility the single-ticket price is sometimes higher.
If you travel on single or individual tickets, on the other hand, the risks of missing a flight are mostly on you, the individual traveler. If you the first flight (SFO > CDG) is cancelled or delayed, the airline will get you to France, but has no further responsibility. If you're late getting the France, you'll miss the second flight, and airline #2 will not be responsible (i.e., will not pay for a new ticket) to get you from France to Warsaw. Worse, after missing the CDG > WAW first leg, the airline will cancel the WAW > CDG second leg.
While flights are usually more-or-less on time, the SFO > CDG flight could be two hours late — not enough to force airline #1 to rebook you or give you compensation, but late enough to miss the CDG > WAW flight, and by extension, have your WAW > CDG ticket cancelled.
For shouldering this risk, individual tickets are sometimes less expensive. Which you choose depends on your personal risk tolerance. Some individual—ticket travelers overnight near the airport of an important (international, expensive, intermittently-scheduled) flight to absorb travel delays and minimize the risk of missing the flight.
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You are considering booking separate flights for your trip. As David indicates, this means that if you are delayed, you are most likely on the hook to book and pay for a new ticket to Warsaw (and usually the return flight from Warsaw to Paris as well).
Tickets booked at the last minute can be quite a lot more expensive than tickets booked in advance. And if travelling during busy periods, you could have to wait a while to get a seat (or, alternatively, they may be very, very expensive).
Any hotels and meals would be on you as well.
Remember that if you have checked luggage, you need to:
After that you’ll have the usual steps of going through security and to your gate before the boarding deadline, but if you make the earlier deadline that should be a piece of cake.
The general rule of thumb is that if you have two flights on separate tickets, you should have at least 4 hours between them, but it really depends on the combination of flights (dictates which terminals you use, check-in deadlines, cost of rebooking a new flight at the last minute, risk that you may have to stay overnight...). For the return flights for instance I would have a LOT more buffer, as check-in deadline for long haul flights are longer, there aren’t many CDG-SFO flights (you’ll probably have to wait until the next day), and such a flight at the last minute will be very costly.
Ideally, you want to have an overnight stay in between, but that really depends on the combination of flights.
As to why search engines don’t usually suggest those flights: