Disclaimer: I don't have hands-on experience with managing this stuff, this is mostly what I've heard from other sysadmins, network engineers, &c.
Assuming that the phone company has connected the phone line/circuit to the ISP, are configurations such as VCI, VPI, modulation and VLAN tag the only details required to connect to an ISP?
Yes.
Actually, with ADSL, ISPs don't have to use VLAN tags because the same operation could be done by using different VPI/VCIs (and the modem can locally map each VPI/VCI to a local-only Ethernet VLAN). But it's certainly possible that some ISPs use VLANs on top of a single circuit, so if that's your situation, you have to specify the VLAN tag as well.
On the other hand, VDSL does use Ethernet VLAN tagging exclusively, (as far as I know), because anything ATM-related has been ripped out so there are no VPI/VCIs anymore.
How do the settings above relate to DSLAM?
Modern DSLAMs emulate the ATM protocol (with VPI/VCI) on the customer side, and translate it to some form of regular Ethernet/IP-based encapsulation (afaik, L2TP) on the ISP side.
In the past (early days of ADSL), I think the DSLAM just did the bare minimum – converting phone line electrical signals – and it was ATM circuits all the way.
Can a modem connect to an ISP without a PPPoE client if a router is configured with the PPPoE settings?
Yes. The modem provides the Ethernet-over-ATM (AAL5) encapsulation/tunnel, and if it bridges the tunnel with your local Ethernet, then it doesn't matter which device generates the PPPoE frames – they still go over the link in the same way.
Indeed in the early 2000's it used to be very common to have the modem as a bridge (sometimes with no routing capabilities whatsoever) and to connect a single PC directly to the Internet, using a Windows-based PPPoE client. (Windows XP had native PPPoE support, for older versions you had things like WinPoET.)
What is the purpose of the PPPoE client?
With ADSL, I think ISPs use it a) for authentication, b) for accounting, i.e. keeping track of which lines have online modems and when, c) for providing configuration such as the IP address.
In any case, PPPoE is not required for ADSL to work. The DSLAM has other ways of recognizing the client – it can just map the physical line to a customer (similar to DHCP Option 82 added by Ethernet switches).
So the same Ethernet-over-ATM encapsulation can just as well carry regular IP/DHCP directly ("IPoE"), and many ISPs actually use this method because it reduces complexity and overhead.
