I got a bundle of Toads from the Toad ticket event, and now I can purchase some items for the town, but it's unclear whether I lose these Toads when I purchase the item (with coins). Are Toads just a condition for unlocking those items, or will I lose them upon purchasing the town item?
No, when you purchase an item the amount of toads that you have is unaffected. The only thing that you need to buy these items are the coins collected in the levels. But when you have more toads, your town will level up and unlock more items to buy. Remember though, all of the buildings are just decorative, and only the special items have a purpose.
You can however, lose the toads that you already have. If you enter a Toad Rally event and are beaten, then the toads that your opponent wins will come out of the amount of toads that you have. So you'll be looking to be losing about 25 toads when you lose.
When buying items in your Kindgom, toads are a requirement rather than a currency. This means when it says you need 20 Red Toads and you have 30, after buying the item you will still have 30 Red Toads.
You can though lose toads through losing a Toad Rally game.
No, you don't. Those are purchased with coins, not Toads. If you have enough Toads, you unlock more items. You can only lose Toads if you lose a Toad Rally event.