Travel grant request letter, should I request maximum travel amount?
It's certainly fine to ask for the maximum, if your expenses are at least that much.  And you can combine multiple expense items, as long as they are all reasonable.  In case 2 you can certainly request $1000.

I would actually go further: list all your expenses and request the total amount, even if it exceeds the maximum reimbursement amount stated.  You can phrase it as something like "My total travel expenses are $2345.67; I understand the maximum grant offered is $1000.00."  Let them take care of capping your reimbursement at their maximum figure.

Part of the reason for this is that organizers sometimes find they have more money, or fewer participants seeking funding, than they expected, and so they can actually give more money to each participant than their originally stated maximum.  So if it turns out that they actually have $1200 per person, they know they can reimburse you for $1200 instead.  If you only mentioned $1000 in expenses originally, they might think that was actually your total expenditure, and you might miss out on the extra money.

A lesser reason is that it helps keep the organizers informed as to what it actually costs people to attend, and how much of a difference their travel grant is making.

Of course, if your total travel expenses are only $534.63, then you should only request that amount (and make it clear that this represents your total expenses).  The point of the grant is to cover your expenses, not to arbitrarily enrich you.