Thyroid $T_3$ Binding: Majority Bound

Thyroid hormones, including Triiodothyronine ($T_3$), circulate in the blood largely attached to specific binding proteins (like TBG) and albumin. Only a minimal fraction, approximately 0.3%, remains free ($T_3$) and biologically active. Thus, the assertion that the majority of circulating $T_3$ is bound is accurate.

$T_3$ Secretion Origin: Thyroid vs Peripheral

The thyroid gland directly secretes about 20-30% of the total circulating $T_3$. The larger portion, roughly 70-80%, originates from the peripheral deiodination (conversion) of Thyroxine ($T_4$) in tissues such as the liver and kidneys. The statement "Only 50% of the circulating $T_3$ is secreted by thyroid" is considered incorrect in the context of this question.

TSH Test Sensitivity in Primary Hypothyroidism

In primary hypothyroidism, the thyroid gland's function is impaired, leading to decreased production of thyroid hormones ($T_3$ and $T_4$). This triggers the pituitary gland to increase the secretion of Thyroid Stimulating Hormone (TSH) in an attempt to stimulate the thyroid. Consequently, an elevated TSH level is the earliest and most sensitive indicator of primary hypothyroidism. Therefore, the statement that TSH estimation is not sensitive is false.

Fetal Pituitary-Thyroid Axis Dependence

The fetal hypothalamic-pituitary-thyroid (HPT) axis develops and matures largely autonomously throughout gestation. While maternal thyroid hormones ($T_4$) readily cross the placenta and are essential for normal fetal development, particularly brain development, the functional independence of the fetal axis means it is not significantly dependent on the maternal axis's activity. Thus, the statement suggesting substantial dependence is incorrect.

Conclusion: Correct Thyroid Hormone Statements

Summarizing the analysis:

• Statement 1 is correct.
• Statement 2 is incorrect.
• Statement 3 is incorrect.
• Statement 4 is incorrect.

Therefore, only statement 1 is correct.