Evolution

In his theory of pangenesis, Darwin proposed that every part of the body produces tiny particles called gemmules (pangenes), which travel through the blood and collect in the reproductive cells.
These gemmules pass to the offspring and carry the characters (including acquired ones) of the parent's body parts. This is why the theory resembles Lamarck's inheritance of acquired characters.
The theory thus suggested that there should be some physical (material) basis of inheritance, carried from parents to offspring.
So according to it, there should be some physical basis of inheritance.

This is the replica plating technique of Joshua and Esther Lederberg.
Bacteria are first grown on a master plate containing complete medium without streptomycin, so mutants are not selected at this stage.
A sterile velvet pad is pressed on the master plate and the imprint of the colonies is transferred to fresh plates, keeping the same positions of the colonies.
According to the answer key, the imprints are used on plates with streptomycin: only the streptomycin resistant colonies grow there, and they appear at positions corresponding to particular colonies of the master plate.
Since these resistant cells were already present on the master plate before any contact with streptomycin, the mutations arose spontaneously and randomly; they were not induced by the antibiotic as an adaptation.
Note: in practice a plate without streptomycin is also used as a control, so this question is open to the other interpretation.

The age of fossils is determined by radiometric (radioactive) dating and other physical methods.
The radio-carbon ($^{14}C$) method is used for fossils up to about 50,000 years old; the potassium-argon and uranium-lead methods are used for very old rocks (millions to billions of years), where the errors in absolute terms are large.
The electron-spin resonance (ESR) method measures the number of trapped electrons accumulated in materials such as tooth enamel and shells due to natural radiation since burial.
According to the answer key of this paper, the electron-spin resonance method is taken as the relatively most accurate method, because it can be applied directly to fossil bones and teeth over a wide range of ages.
Note: many textbooks regard radiometric methods as the most reliable, so this question is debatable.

Lederberg and Lederberg grew bacteria on a master plate of complete medium (which supports all bacteria).
Using a velvet pad, they transferred (replicated) the colonies onto a plate of complete medium containing streptomycin.
Only colonies that were already resistant grew on the streptomycin plate, and the matching colonies on the master plate (never exposed to streptomycin) were also resistant.
This showed that resistance mutations arise spontaneously before exposure, and the antibiotic only selects them.
So complete medium and streptomycin are used to obtain the streptomycin resistant strain.

Most new mutations are harmful or neutral; only a few are beneficial.
If harmful mutations accumulate in a population, the offspring may be less fit (less adaptive) than their parents.
Natural selection and adaptation increase fitness, so they cannot be the cause.
So, as per the answer key, the next generations become less adaptive than the parental generation due to mutation.