Explanation
Statement I is correct - since forward prices are determined as (Spot - PV of dividends)*e^(rt), an increase in dividends will reduce forward prices.
Statement II is incorrect as forward prices will be determined by near term interest rates, specifically by the borrowing rate for the period of the contract, and will stay unchanged if near term interest rates do not change.
Statement III is incorrect. Futures exchanges require both buyers and sellers to deposit initial margins as prices can move adversely for either of them.
Statement IV is incorrect, as the margin deposited when a contract is entered into is called initial margin.
Margin calls thereafter resulting from movements in prices are called variation margin.
Statement V is incorrect. Most futures exchanges distinguish between hedgers and speculators and require different margins from each.
Statement VI is incorrect. Interest rate futures behave almost identically to their bond counterparts, and carry both duration and convexity.