Step 1: Understanding the Concept:
Boiling point depends on intermolecular forces. Generally, for a group of similar molecules, boiling point increases with molar mass due to increased Van der Waals forces. However, strong interactions like hydrogen bonding can cause anomalies.
Step 2: Detailed Explanation:
1. Analysis of Statement I: For Group 16 hydrides, $H_2O$ exhibits strong intermolecular hydrogen bonding. This results in an exceptionally high boiling point compared to others. The actual order is: $H_2S<H_2Se<H_2Te<H_2O$. Statement I says $H_2O$ is the lowest, which is **Incorrect**.
2. Analysis of Statement II: While the boiling point increases from $H_2S$ to $H_2Te$ as molar mass increases, the trend is broken by $H_2O$, which has the smallest mass but the highest boiling point. Thus, as a general rule for the entire group, the statement "boiling points increase with increase in molar mass" is **Incorrect**.
Step 3: Final Answer:
Both statements are incorrect due to the anomalous behavior of water caused by hydrogen bonding.