= Solution
Use a common comparison for all of question2: retain the same number and height of fuel rods and approximately the same normalized rod-power shape; reduce <fuel lattice pitch> by making the active core cross-section smaller. Compare otherwise similar operating states of an initially <under-moderated reactor>, typical of a <pressurized water reactor>. Rod number, core height, reflector and control settings are not all fixed explicitly by the question, so these are stated assumptions. Keeping the external core envelope fixed while inserting more rods would be a different comparison.
\b[<Reactor reactivity> normally decreases at unchanged controls and reference temperatures.] Less water per fuel atom reduces <neutron moderation> and increases resonance absorption during slowing down. Reduced absorption in the water partly compensates, but on the under-moderated side the net lattice tendency is lower multiplication. This is the usual under-moderation argument, rather than a universal rule for arbitrary fuel lattices.<Nuclear Physics and Reactor Theory, Volume 2 by the United States Department of Energy>[Module NP-03, pp.24–25, Moderator Effects: competing resonance escape and thermal utilization]{ref}
\b[<Neutron leakage> would usually tend to increase.] The smaller transverse core extent increases the geometric tendency to leak, and reduced moderation generally increases the slowing-down distance. There are competing changes in fuel absorption, transport lengths and reflection. Thus a definite leakage fraction needs the actual core and reflector arrangement; the usual increase is a qualitative tendency, not a geometric theorem for every redesign.
\b[The <Doppler coefficient of reactivity> remains negative under the ordinary uranium-fuel assumptions.] Increasing fuel <temperature> broadens absorption resonances, increasing effective <uranium-238> resonance capture and reducing <reactor reactivity>. This stabilizing fuel-temperature effect is distinct from moderator-density feedback.<Reactor glossary by the United States Nuclear Regulatory Commission>[Doppler coefficient entry: increased uranium-238 absorption as fuel temperature increases]{ref} Greater importance of resonance absorption can make this feedback more important in a tighter lattice, but \b[its change in magnitude is not fixed by pitch alone]: spectrum, resonance self-shielding, fuel composition, burnup and the reference fuel <temperature> all enter the derivative.
\b[The fraction of fissions in <uranium-238> tends to increase.] The harder neutron spectrum gives more opportunity for <fast fission> before <neutrons> slow below the uranium-238 fission threshold. This concerns the fraction of the total <nuclear fission> rate, not an assertion that the total thermal power increases; that power is held fixed.
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