The type of options package (introduced in question 1) depends on whether the underlying is a rate or a fixed-income instrument. A general statement claiming that caps are equivalent to call options is not correct and requires further analysis of the underlying.
Selling a cap on a bond you’ve bought is like selling a call option on the bond, since it limits the upside potential for the investor, and therefore demands a premium on the cap/option, or a discount on the bond.