No need to abuse mod. It's a bit of an woopsie for 1st timer to have messed up lockpicks so it cant be helped.
It's a bit too long so I dont remember correctly. But in Poland there's a few random encounters that provide us with engineer items. One map give doctor items, mostly great bloods. So wander around it to see.
The lockpick maps seems to be a factory location I think~ Not sure.
EDIT: check my note. the supply refresh after certain main campaign missions. engineers and doctors stuffs are obvious, but ammo is not, as they change according to campaign (axis get german/axis ammo). So if you like an axis weapon in an allies campaign, take careful count of ammo and ability to restock it. And vice versa.
On training skills. Game use train-by-use scheme, with levelcap. You can totally raise your skills to current ceiling by training in random missions. Especially engineer skills, since arming windows and doors need a high number of them (just arm, not disarm).
On proficiency. Use much of one class of weapon and you raise familiarity. Like, if you use your kukri much, you will raise its FAMI stat. high stat allow much better damage, hit percent, and crit. So train the new weapons in random mission. Especially your sniper's gun. You wont have much chance to use it much in campaign, so train them outside.
FAMI also divide by class I think. Rifle, SMG, pistol, and heavy machinegun. Knife, throwing weapons. Say, you got your Lee Enfield Fami to 10. Now you want to change to SVT10 scoped, you need to lower LE's FAMI to 0 before SVT10's start to grow. You can use a quickshot carbine rifle to lower FAMI quick and change to SVT to raise, also save on russian ammo.