What cargo do you have that you want to keep? Only modular terminals are worth holding, and you've already unlocked qwent, so I can't imagine it's those...anyway...
When you get to Prof Palin, you will find that he can modify Thrusters AND FSD (FSD only to grade 4 I think, but it's still useful for levelling him up). Don't have the impression that you have to level him up with useful upgrades, just bang through them. If you are level 1 with him right now, then do ANY level 1 recipe that he can do, three times (hit try again twice then DISCARD the third result) to unlock level 2. Now scroll through the things at level 2 until you find something you have mats to do three times to unlock level 3, then scroll through level 3, do whatever you can do 3 of, then 4, and bang, you are at level 5 in only 12 rolls using whatever mats you have.
Then go straight for G5 Dirty Drives, level him in one go using ANY materials you have in stock. The same goes for all the other engineers, speed level them by doing whatever recipe you have mats for, then discarding the results, you need to do a recipe at the current level three times to unlock the next level and you don't have to apply any of the upgrades, you can discard them and still get the progress.
Most engineers also have an outfitting screen where they sell examples of modules they can modify, they don't always have a good range, but enough to buy a couple of items just to waste materials on to level up the engineer.
For learning where materials can be found, use
https://inara.cz , click on the 'Galaxy' link at the top, then one of the Engineers sub menus, search components for the component you want and it will tell you the most common ways to obtain it. Usually, this is more useful that the description provided on the right panel in cockpit as it is more fine grained info.
For chromium and any other elements you need, use eddb.io and search 'Bodies', enter the material you want in the form, and try to find a high metal content world or better a metal rich body, that has what you want. You ever done any prospecting?
Lastly, don't forget there's a way to easily get a large number of mid-grade materials. Head to the Naphtha Tanker, it is currently in Okinura system, go there, go to it, you can't miss it, and when you drop out next to it, you will find materials floating in space. These are randomly generated from a table, so can change each time you visit. You can then either log out and back in again repeatedly until you've found all you need, or leave and reenter the instance via supercruise to reset the materials. Not all materials can be found there, no data for example, and no grade 5 (ultra rare) materials either, but several grade 3 and grade 4 'manufactured' materials are best farmed there.
P.S. The Naphtha tanker moves every so often, it's itinerary is public domain, so if it's not in Okinura, it will be in its next destination, always close to the heart of the bubble.