How to get detailed information for a particular cryptocurrency?

Use the /coins/{id} endpoint for this.

Get info like image/logo, price info, market cap, trading volume, coin description (and in all languages supported)

Other info like all time high/low, 24h changes are also available.

Can I get a list of tickers for a coin on a specific exchange?

Yes - use the /coins/{id}/tickers endpoint, and specify the coin_id while leaving exchange_id empty.

Example: https://api.coingecko.com/api/v3/coins/bitcoin/tickers

Can I see all the places where a coin is traded on?

Using the /coins/{id}/tickers endpoint, enter the coin_id and exchange_id (list can be found at https://api.coingecko.com/api/v3/exchanges/list).

Example: https://api.coingecko.com/api/v3/coins/bitcoin/tickers?exchange_ids=gdax