@01189998819991197253 Think it's going to be hard to hit ALL the points.
The cheapest fountain pens are probably Jinhao, but nib QC is all over the place. Pilot has the most reliable nib QC, but the price for a Kakuno may be slightly out of budget. Could also consider the Platinum preppy, but they have more feedback than Pilots.
Not sure on mm widths. Finding larger than an M nib for any of the above is difficult or nonexistent.
All accept cartridges & converters.
@01189998819991197253 they come in sizes like extra fine (EF), fine (F), medium (M), broad (B), sometimes double broad (BB), also stub.