Andy, first things first.
Who is the "someone" and who are "some people"?
Are these in the chain of command?
If they are not then my advice is to develop tactics to either ignore them or shut them up.
If they are management then an explanation is needed and a discussion on the standards of bikes that you will be selling.
Now, here's the thing. You may find yourself having to compromise so my suggestion is to prepare well for any discussion, preferably with examples. For instance take a bike and explain the issues with chains, cassettes and cables.
As regards your specific questions:
Tools: They should be the best you can afford. Anything else is false economics
Consumables:
Cables: Damaged or frayed should be replaced. Sticky or gunky may be cleanable. What about the outers?
Tubes: I agree absolutely about matching valves but don't understand the reluctance to use patches. All.my tubes are patched, often several times
Chains & cassettes:
You need a chain wear tool!! That is just a simple example for any discussion on standards. The fact that you bought your own is only relevant to the point that you don't have all you need.
As for cassettes (and I am far from an expert) some people can judge the life in a cassette by looking at it. Yes, a worn chain might have worn it more but there may well be a lot of life in it yet. Selective reuse could save €s.
Dynamo systems: Again, you need a proper tool. It's basic arithmetic. Is there a source for cheap wire? Perhaps I'm wrong but I can't see that as being expensive?
The stock you are building up, is that new or recycled? If new do "the people" understand that the stock is waiting to be used and to add value?
Specific parts: if you need them you need them. However, do you really need them? Is the bike functional and safe without them? Or can you price the bike without (eg chain guard) and on the tag offer a price including the chain guard?
Don't worry about the things bought that are not needed right now. We've seen some of the pictures of what you inherited
.
As for your plan......
You're organising the shop so step one is the current management priority.
I think the "pair" system looks better on paper than the reality will be. It must be frustrating to work on a bike this week, get new parts and then find usable parts on a bike next week.
Perhaps, like in an emergency room a sort of "triage" process will help when the bikes first come in?
Probably best to hear from people with experience in this kind of thing, though. I would imagine there is always going to be an efficiency Vs effectiveness friction.
Going through invoices with people who are not used to bikes may be a frustrating experience. I'd imagine the clearest way to communicate is to take an example bike and go through the process with them. Explain the frayed cable. The worn chain. The fact that you can't be sure that the dynamo wire is good or not, hence replaced. It's Germany - the lights have to work. Show the costs and expected sale value.
Next time "someone" starts complaining figure out if they are someone to listen to it not!
I'm finding the general situaion rather stressful,
If we are talking about other people commenting (not management) then this needs to be said to management!
If it is management then a discussion is required.
To be fair, you have said yourself that some of your prices may be too low. Couple that with "the new guy" buying much more than the "old guy" and I can see where "people" would enquire.
One possible way out is to look at the achievable sale price of a bike and then assess the cost of making it ready for sale. Presumably there's a margin of profit required. Include that in the calculation.
If expenses mean that the margin cannot be achieved then the bike is shelved.
Another way is to have two similar bikes, one with new components (or as many as needed) the other not and both priced accordingly. Customers have a choice and understand why one is cheaper.
As you say, this is all "management" stuff and very far away from what you are used to.
Deep breaths and good luck!