How do I mount the serrated paper guide in the back? There's no space

Being an older mech with a static part in front, I don't have an exact answer for this unit, but it looks like HP designed it for a top-down install, making the reinstallation of this piece a bit of a process. See if you can find a way to move the paper sensor/pickup assembly forward without damage. That said, you might have a shot at starting from the bottom to adjust the bottom pins and then angling it until you get the top part.

HEADS UP: I've done it without disasssembly before to salvage a CS431 with a missing duplex sensor on the fuser that threw errors about it in my testing (right side, part of the fuser). If you can't get the tab from a donor fuser, the only other way to get the part (economically) is to buy a C3224 needing toner (3 toners=new printer cost with a page yield that is generous; 1,500 pages, the "C32" toner is junk). The only way to make this work wthout wasting a printer is if you can get a replacement fuser individually for much less. For the C/MC3326 It's usually more cost effective to gut a C/MC3224 for the fuser. The C/MC3426 tends to fare better due to the high yield toner making them viable as a useful printer. In general, CS models tend to fare far better and may be viable to do the fuser swap if something like that occurs without wasting a loss leader variant like with the C/MC3326. The CS431 was just my attempt to avoid buying a fuser.

Repairs like the sensor reinstall CAN BE done without opening it, but the dexterity needed to avoid taking the printer apart required patience can be... a lot. When I tried it on my CS431, I was prepared to open the printer since I know how to work on them given I have had a C3426 (died early, bad controller), my initial C3326 with (uncorrrectable CMY reg issues, even after 2 tries with 2 full toner sets), a standby C3326 with unrepairable issues and the current C3326. IF it didn't work, it wasn't worth risking the tab to avoid taking some panels and screws off.

The issue now is the sensor placement is so poor that proper access to the print mechanism to reinstall this part may not be possible without a full teardown. Or it fell out due to plastic fatigue, causing it to come out just enough. The design makes me think it has that style mechanism if that part is static and NOT readily movable.

READ: Looking at the condition of the rollers, this printer is probably near the end of its life anyway. Those rollers are shinking and heavily stained with heavy wear. There's NO replacement for them outside of a new mech (which is almost certainly NLA), unlike the bulletproof pre-HP DS lasers like the M401 where you can do a roller wap for ~$25-30 for both Tray 1 and Tray 2. It may be just about that time for a new machine either way if you can't get this done (buy a Canon, not another HP). 10 years is a lot on an inkjet like this, so the poor condition of the rollers doesn't shock me.