Do free-trade agreements typically include clauses relating to services?
For example, reciprocal recognition of professional qualifications.
The simplest answer is: some do, some don't.
Trade in goods and trade in services are dealt with quite separately, so structurally, you wouldn't find a couple of clauses on services within an FTA. You would generally find a chapter on goods and (possibly) another on services, reflecting the division in the WTO between the GATT (goods) and the GATS (services).
Quantitatively, there is a roughly equal split between goods-only agreements and agreements that cover both (153 for goods only and 154 combined agreements have been notified to the WTO as of December 2018).
You also often find a group of countries negotiating a goods-only FTA first, then extending to cover services later on (for example by adding a protocol to an existing treaty). This reflects the fact that an integrated services market is usually seen as a "deeper" form of integration than tariff-free trade.
No, but there is a proposed free trade in services agreement on the table, but reciprocal recognition of licenses isn't intrinsically part of it. However, it does have a provision that once a trade barrier is dropped, it can never be reintroduced in some form. So, for example, a Canadian physician cannot practice in the US and vice versa automatically, but under the proposed treaty, if the two nations acknowledged the validity of each other's licenses, then they could never reverse that decision.