My question is what was the first 100% PC compatible with these basic I/O features built-in on the motherboard?
This question is a bit tricky, as it adds several constrains. For example requesting a parallel port isn't all that logical, as back in the early 1980s the race for the 'right' printer interface wasn't as decided as 10 years later. But let's see the candidates.
Sanyo MBC-550 of spring 1982 - calling it compatible might be borderline. It did feature parallel port, floppy controller and graphics direct on board, with the graphics partial CGA compatible. It did not feature an ISA bus, but a custom pin header for up to two stacked I/O (one offer was a true CGA compatible board). Missing an on board BIOS, software compatibility due the disk loaded BIOS was poor at first, but improved quite a lot later on. Another hurdle for full compatibility would be the slower CPU speed of 3.58 MHz.
Columbia Data Products MPC-1600 of June 1982 - while being a true compatible and including parallel and serial interfaces and floppy controller on board, CRT was still handled via a standard ISA card.
Columbia Data Products MPC-VP in 1983 followed the same scheme, just this time portable.
Olivetti M24 in 1983 - while highly compatible, it wasn't a 100% at least due it's 7 MHz 8086. Also the design wasn't a single PCB but kind of a stacked one with the main board on the bottom, the I/O board on top, both connected via the video board angled at 90 degrees. While it's not a single PCB, they are no separate available add-on cards either.
Compaq Portable in March 1983 - a true compatible despite a somewhat different graphics 'card' design combining features of CGA and MDA. Notably the first with a BIOS as compatible as possible. The Compaq Deskpro moved that concept to the desktop.
IBM PCjr in March 1983 - while integrating many features like joystick ports, sound and a serial port, the floppy controller was still on a separate board - one of the bad design decision around the Peanut - even though not necessarily the reason for its failure.
And then there is the Tandy 1000 series which offered all in one machines in many configurations, starting in late 1984.
Before deciding, honourable mentions, due being less than compatible, should got to
Sirius 1 of 1981 - at the same time as the PC this machine already included a faster CPU, more RAM, HD Audio, 800x400 graphics and 1.2 MB disk drives.
DEC Rainbow 100 of 1982 - as an example for ambition and failure of a large player
Apricot PC of 1983 - maybe the slickest of all (early) PC-alikes. Especially with the later F1 and Portable (*1,2)
Amstrad PC1512 of 1986, Olivetti Prodest PC1 of 1988 and Schneider EuroPC of 1988 as examples of later consumer/home computer orientated all in one PC-alikes
So, who was the first to fit all these criteria?
Hard to tell. Personally I'd vote for the CDP MPC-1600 by fulfilling the 100% criteria and integrating everything except the video card, which does make sense. Going by the wording it must be the Compaq Portable
Also, how did they "fit it all" given the legacy of off-the-shelf only components?
That wasn't a big deal, considering that the original PC was neither high integrated nor really dense packed. Much of the circuitry could have already back then improved by PALs and GALs without increasing the cost. The Sirius 1, debut the same time as the PC, is a prime example what was possible.
*1 - Most notably here the usage of an 8089 IO-processor.
*2 - To some degree the later Acorn Archimedes continued that design.