And to answer your other questions about fees, there are a number of sites that compare brokers' fees, Google "broker fee comparison". I like the Motley Fool, although there are a lot of others. However, don't go just by the comparison sites, because they can be out-of-date and usually just have the basic fees. Once you find a broker that you like, go to that broker's site and get all the fees as of now.
You can't sell the shares that are in your Charles Schwab account using some other broker. However, you can (possibly now, definitely eventually, see below) transfer the shares to another broker and then sell them there. But be aware that Charles Schwab might charge you a fee to transfer the shares out, which will probably be larger than the fee they'll charge you to sell the shares, unless you're selling them a few at a time. For example, I have a Charles Schwab account through my previous employer and it's $9.99 commission to sell shares, but $50 to transfer them out. Note that your fees might be different even though we're both at Charles Schwab, because employers can negotiate individual deals. There should be somewhere on the site that has a fee schedule, but if you can't find it, send them a message or call them.
One final thing to be aware of, shares you get from an employer often have restrictions on sale or transfer, or negative tax consequences on sale or transfer, that shares just bought on the open market wouldn't, so make sure you investigate that before doing anything with the shares.