How do I keep track of what event a particular scout paid for when they make a deposit?

Deposits to member accounts are not linked to events.  When you charge a scout for attending an event, it reduces the value of his account by that amount.  When the scout makes a payment to the troop, that deposit increases his balance.

An individual member account is like a credit card account.  When you make a payment to Visa, you don't pay for a specific item on your bill;  your payment simply reduces the total amount you owe on that credit card.  In the same way, payments from troop members do not get posted directly to an event, but simply increase the funds available to that member (or reduce the amount he owes the troop).

We do provide the option of noting the event for which a payment was intended.  This does not post affect the balance of the event, but serves as a "memo" to indicate the intent to pay toward that event.

But my troop requires that all scouts pay for an event before the event occurs. How do I handle that?

If you require scouts to pay for an event in advance, create a Charge Troop Member Account For Event transaction for each scout who plans to attend.  This will reduce each scout's balance by the cost of the event.  Payments can then be received and deposited into each scout's account.  If you then view Individual Balances or Report Account Balances, you can see which scouts have negative balances and thus have not yet paid for the trip.

You can also view the current account balances for each participant in an event from the Troop Calendar by configuring your User Roles to be authorized for the "View Participant Individual Balances on Event" task.

As noted above, you can also configure transaction types to allow deposits to reference the event for which they are intended. This does not affect the balance of the event, but these payments can then be viewed when you display the participants from the Troop Calendar.  If you use this feature, you will need to set a policy that determines whether a member should be allowed to attend an event if they have a negative balance in their account (i.e., they owe the troop money) but made a payment intended for that specific event.

How do we use the system to keep track of troop assets, like the value of merchandise we are selling for a fundraiser?

Most troops do not need to track assets and liabilities.  After all, a troop is not a business.  When you need to buy a few new tents, you hold a fundraiser or ask the members to chip in, and that's that.

However, it is possible to use the fund accounting feature to set up various asset accounts.  While we do not encourage this, with enough creativity you may be able to define the necessary categories, funds, and transaction types to make this work.