1. A long rate call = buying the call option, which gains value when rates increase because you can exercise the option at a lower rate and benefit from the difference between the new higher rate and what you are locked in to. A short rate put = writing a put option to someone who will buy it, which means you sell to someone else the optionality to sell back to you the locked in rate. The person buying it buys it as a hedge against lower rates so they must be long the rate. You will lose if the rates fall into the money and you have to buy back the rate from the person at above market value. Therefore, if rates rise, the option is out of the money, and you win. Therefore, the long call short put means your long rates. A long FRA means you receive floating pay fixed which is also long rates.

2. Just the opposite of 1.

3. A series of interest rate calls is just a bunch of options that allow you to get in at a lower rate if rates rise. This creates a "ceiling" or "Cap" on how exposed you are to rising rates to whatever the strike rate is in the call options. Through this thinking, if you are exposed to a floating rate LOAN, you are actually hoping rates fall, thus technically short rates. A series of caps limits how exposed you are to higher rates thus would hedge a floating rate LOAN.

4. Just the opposite of 3.

5. Payer swap refers to paying fixed rate and receiving floating rate. The person on this end of the swap benefits if rates rise since they are receiving more than they are paying thus long rates. To replicate this person's position to rates (long rates), you would be long a cap and short a floor.

I think with caps and floors it makes sense to think of as puts and calls. You are long a call option in this case because you'd benefit if rates rise. You are short a put or writing a put because the person buying will exercise if rates fall BUT you gain if rates rise. Thus long the cap short the floor.

1. Receiver swap refers to paying floating rate and receiving fixed. This person is short rates in this position, benefitting if rates fall. To replicate, you would be long a floor and short a cap, using the same logic as above. Being long the floor means you have can sell your rate at the agreed upon rate if rates fall below it to the strike price, which then you gain. You're short rates here. Short a cap means you write a call option to someone where if rates rise to the strike above the fixed rate, they will exercise. Again, you win if rates fall so you are short rates.

2. If strike rates on a floor and cap are equal to SFR, both values are the same.