Resistors in series
Series resistances add directly. Four 1 kΩ resistors on 9 V total 4 kΩ and pass 2.25 mA, with each resistor dropping 2.25 V. The voltage across any one resistor is its share of the total resistance.
How to total a series chain
The practical use of a long series chain is a voltage ladder: a string of equal resistors tapped at each junction to produce evenly spaced references, which is exactly how a flash ADC or a simple resistor DAC works. Tolerance behaves better here than intuition suggests: random errors in a long chain partly cancel, so a ten-resistor ladder of 5% parts has a total closer than 5% off, even though any individual tap could still be out by the full amount.
Questions
R_total = R₁ + R₂ + R₃ + … Nothing more complicated than addition.
In proportion to resistance. A resistor that is a quarter of the total drops a quarter of the supply.
For the same supply, parallel — because the lower total resistance draws far more current.
To reach an unavailable value, to spread heat, or to create intermediate tap points.
Worst case yes, but in practice random errors partially cancel across a long chain.