Today almost all ISPs use a NAT system to assign more people the same IP (at least where I am), probably because the IPv4 addresses are ending and they want to save money. Is it possible to make a DoS / DDoS attack on such a connection? Knowing the public IP address, I think theoretically it is possible to saturate the ISP circuit that uses NAT, but practically it is possible to attack only the single target? Also because I believe it is impossible for anyone with such a power to saturate the entire ISP.
Saturating bandwidth capacity of an entire ISP is very well possible and unfortunately happens on a daily basis. You’re right that with techniques like carrier grade NAT and end user may not have a dedicated IPv4 address, but that can still result in an outage when attacked. And of course, if the ISP deployed IPv6, it can be possible to uniquely target the end user that way.
Answer is yes, it's possible even you are behind a NAT. Because the DDoS attacks vary from network level attack like ping of death to application level attacks.
You may be lucky if your ISP has implemented Anti DDoS protection on their gateway level (most of them does these days, at least for basic attacks like ping of death, high packet rate attacks, etc).
Well it depends. Without any explicit DNAT rules, you cannot be reached directly behind the NAT, but only after an initiated connection has been initiated from your side. However, I'm not quite sure whether the question makes sense, because when the NAT entry/exit point is DoSed, then you will also be affected, since it is your route to the Internet.