Sentence Correction

Your doubt is pertaining to the usage of rate in two different capacities.

Rate of is used when we have to express "measure"
For example: Rate of change in commodity prices is indicative of a highly volatile market.
Here we are using "rate of" to express "measure".
The sentence implies that the measure of change in commodity prices is indicative...

Rate for is used when we have to express "price"
For example: Rates for gold have been consistently increasing.
Here it is clear that we are talking about price of gold.

So when you see the word - rate, see if you can replace it with price. If yes, then you must use "for" with rate.
However, when it makes sense to replace "rate" with "measure", you must use "of" with rate.

Now coming to the sentences in your post:
1: Rates of liability insurance have risen.
Clearly here we are are talking about prices of liability insurance. So the correct idiom is "rates for"
2: Prices of beach side properties fell drastically
Yes this is correct. But we have to use "rates" here, we will use the idiom "rates for". This is just idiomatic usage that you will need to remember.
Rates for beach side properties fell drastically.
3: The rate of fluid loss is under control
Yes this is correct. Here we are using rate in the capacity of fluid loss. Measure of fluid loss is under the specification limit.
4: The interest rates of government bonds are very high.
Yes this is correct. Now note here that you are using "Rates". You are infact using "interest rates" which does not function like "rates". You are talking about a characteristic of government bonds - interest rate.

For e-GMAT customers, the idiomatic usage of "rate" is covered in detail in the concept titled - "Idioms - Functions - II"

Thanks,

Payal

Great job @Pramendrapandeya in explaining the usage of rate of and rate for.
Just adding a couple of examples:

As you said, 'rate' can be used with two different prepositions and carries very different meanings.

When rate is used with for, it means price charged. For example:

Rate for insurance coverage have increased over the last 2 years.

When rate is used with of, it implies measure. For example:

Rate of change of stock prices indicate the extent of volatility.

Hope this helps.
Regards,
Payal