If you are on a shared internet connection, you are behind a LAN. In this case, it appears to them as if you are all coming from one single computer. They should be unaware of who is torrenting. However, there are advanced methods by which it may be possible to tell, remotely, which computer is responsible. Computers' networking stack has a partially-unique TCP fingerprint, which can be detected passively with tools such as p0f. Information such as the operating system and version, system uptime, and more is revealed through this connection. Additionally, torrent clients give away a large amount of information, like web browsers. So while the IP and port does not give away which computer is torrenting, TCP fingerprinting may. It's unlikely that such information will be used against you though. They would need to know who owns what computer in your house, and what computers are there in the first place.
There's also the issue with ipv6 which can send the MAC address over TCP which uniquely identifies each computer, but I don't believe any modern OS implements this optional feature, so only your router is aware of the MAC address of each individual device.
To answer your other rather scattered questions...
Also, what are internet provider’s stances on torrenting?
In the past, some of them tried to block it entirely by inserting RST into the stream, which caused the connection to break (ahem Comcast). Others just slow it down slightly to prioritize other traffic. Most just don't care as long as you don't exceed your data cap.
Is it likely the landlord received a notice about copyright infringement and not about torrenting in particular?
That is likely. I don't know of any cases where people have gotten in trouble for simply torrenting. It's simply a method of file distribution utilizing the peer-to-peer paradigm.
Even though torrenting isn’t illegal, does internet providers try to block it because it’s hard on their system?
That's a common excuse they make, but torrent traffic dwarfs the amount of traffic which originates from Netflix, Skype, etc. They often get pressure from MPAA, RIAA, and copyright trolls to crack down on torrenting.
Out of curiosity, how do they know someone was torrenting?
There are many ways, so I won't go into all of them now. Most likely, you connected to a torrent which was monitored by a copyright troll on behalf of some big company. By design, the torrent's tracker has to know all the IPs of everyone connecting, and anyone can ask the tracker for a list of IPs. In fact, that's the only thing the tracker does. It records a list of IPs and the chunks each peer has, along with some other information about each peer. The copyright troll just scrapes the tracker for a list of IPs, then sends a notice to the ISP of each of those IPs. Your landlord got that notice and then told you. It's very unlikely that your ISP itself was actively looking for torrents. They typically don't know or care, unless they are getting pressured by other groups to do so.