Solution go to problem
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Q1:
It should use the call option with the exeercise price $0.00756. The future price of Yen is expected to be $0.006912 which is much lower than the exercise price. The interest of the firm is to safeguard against any adverse movement in price and take advantage of price movement in expected direction.
The volatility in the market has increases leading to higher cost of the option.
The total option premium for option with exercise price $0.00756 is $1,890.00
The amount paid for yen if option is exercised $94,500
Maximum amount to be paid when the call option with exercise price $0.00756 $96,390.00

The total option premium for option with exercise price $0.00792 is $1,417.50
The amount paid for yen if option is exercised $99,000
Maximum amount to be paid when the call option with exercise price $0.00756 $100,417.50

Thus by paying an extra amount of $472.50 the firm is able to reduce its maximum exposure by $4,500
Hence it is advisable to buy the option with exercise price $0.00756

Q2
It Blades leaves its position unhedges the company is expose to currency risk. There is no upper cap on the amount which the company may have to pay after 2 months. If the price movement is in favorable direct the company will make gains but if it is the reverse direction it will make losses and the amount of loss is unlimited. By buying call options and paying $1,890.00 the firm is able to put a cap on the maximum amount it is going to pay.
By paying an amount of $1890, the firm has fixed its maximum liability to $94,500
However, if the future exchange price is low, the firm will not exercise the option and will enjoy the lower price, so in that case the cost of this safety net is $1890.
The trade of is between current $1890 and future unlimited loss if the yen price appreciates sharply. It is advisable not to leave the exposure unhedged

Q3
Since there are speculators in the market who would like to take advantage of any arbitrage opportunity, any such opportunity will cease and the future price of the Yen will be a true reflection of spot price at a future date (ignoring the interest cost on the margin money to be invested on future)
Thus the expectation on order date of the yen spot rate by the delivery date =current future rate $0.006912

Q4
If firm shares the market consensus, the best strategy is to remain unheadged
Total cost under call option
Amount paid for Yen $86,400.00
Call premium $1,417.50
Total cost under call option $87,817.50

Total cost under future hedging
Amount paid for Yen $86,400.00
Total cost under future hedging $86,400.00

Total cost when unhedged
Amount paid for Yen $86,400.00
Total cost when unhedged $86,400.00

The cost under unheadged and future contract are shown as same here but in reality the cost of future contract will be higher as there will be interest which needs to be paid on the margin money to be maintained. Thus going by cost the best option is to remian unheadged.

Q5:
No the option may not tyurn