You can use "I want"+ infinitive in the same way as "I'd like"+ infinitive in this situation, however "I'd like" is a more polite expression.
Other examples are:
I'd like to speak to Mr. Shimizu, please.
I'd like to see the menu, please.
Where will you be leaving the car?
The speaker uses "will"+be+verb-ing to imagine now what will probably happen in the future.
Other examples are:
I'll be working in Spain next year.
I'll be visiting Italy in August.
"Can I" + infinitive is used in this expression to ask permission for something. You can use "could I" in the same way, which is a little more polite.
Another example is:
Can I have your name, please?
Could you show me your driving licence?
"Could you" + infinitive is used in this expression to make a polite request. You can use "can you" in the same way, but "could you" is more polite. The expression "driving licence" is used in New Zealand, Australia and Britain.
NB : However, in American English people say "driver's license".
Other examples are:
Could you repeat that, please?
Could you send
me the information by e-mail?
The clerk is asking whether Ms. Hasegawa will be paying her bill by cash, traveler's check, or credit card.
NB : British English spelling -- 'traveller's cheque'