Yes, I use coinbase and binance quite frequently to exchange cryptos. Also in the United States you can use Robinhood.
The key drawback to Robinhood I have found is you can't transfer the cryptos once you purchase them. It would be more for long term investments of a single crypto or if you want to do some buy low sell high type trading within the span of a day. It is really easy to use and gives you access to some of the major cryptos like LTC, BTC, and ETH.
Coinbase is another app that is really easy to use and it does a good job of keeping track of what you are buying and selling. Additionally, it sounds like they are getting ready to add a bunch more coins to it. Already you can buy/sell LTC, BTC, ETC, BCH, and I think one or two other ones.
These are great tools for starters and have worked really well for me.
Binance is a little more complicated, but it is very versatile and will give you access to many more cryptos. Usually if you want to expand beyond the three main ones you will want to purchase some BTC/LTC/ETH and then exchange it for the actual alt coin or token you are looking at.
Yes I have, and I basically use a combination of these apps on my iPhone/iPad:
Luno: for buying Ethereum and Bitcoins using Euros
Jaxx: as my cryptowallet
Cryptopanic: for informational uses
Cryptofolio: to keep track of my losses (or gains, but these days mainly losses)