I've been having a problem with NPC employees in OFB. There does not seem to be any way of getting them to increase their skills. When I've used my own sims to work in businesses, naturally I can increase their skills at home, but is there any way of increasing the skills and talent badges of NPCs?

I have only townies working in my sims' businesses and they always skill. Not sure if that's how it should be or it is just because of the skilling on community lots hack I have.

I've always known the NPCs to build their skills while working. I don't know why they wouldn't unless there is some glitch.

Just assign them the role of working at the cashier desk or sales, and as they work they will build the skill and eventually earn the first badge - bronze. Then they will earn silver, then gold. Be careful though; as they move up in badges, you will most likely have to increase their wages (if you had their wages set to "fair", and they then get a new badge, their wages will go down to being "unfairly paid" or something similar). As to skill points, they're not really needed to run the business although they can come in useful - however, the more skill points they have, the more you will have to pay them - even if those skills (or even badges) are not needed for their job.

The talent badges are not a problem, it's the individual skill points. For example, I am currently trying to train up an employee to take over as chef in my bakery-cum-cafe, as another Sim is at the level where I can make them a manager, but as she is an NPC, it's not like I can train her up at home, and as she has no cooking points, the meals she can prepare do not give her
A) dessert options
B) adequate time to gain skill points
and getting her to cook other meals is a waste of my profits

If the meals she is cooking is not enough time to gain skills, then she will still gain points, just very slowly.

You could always try cheats. InSim is good, it allows you to click on any NPC sim, gain control of them (select "Make... selectable"), and then you can spawn the "skills adjuster" to add any amount of skill points you want (or remove them), then click back on your own Sim, then click back on that NPC sim then select "Make... unselectable."