Step 1: Understanding the Concept:
Cytological and tetrad analysis (e.g., in Neurospora) demonstrates the exact meiotic stage and recombination kinetics of crossing-over.
Step 2: Detailed Explanation:
1. Statement I is TRUE: Crossing-over occurs between non-sister chromatids of paired homologous chromosomes during the pachytene stage of Prophase I, when each chromosome is replicated into two chromatids, forming a four-strand tetrad structure.
2. Statement II is TRUE: Because each single crossover event involves only two of the four chromatids (leaving two non-recombinant parental strands), the maximum theoretical and observed recombination frequency between two linked loci cannot exceed $50\%$.
Step 3: Final Answer:
Therefore, both Statement I and Statement II are true.