How are these different-speed switches internally connected?
There's no standard way. Also, it doesn't really matter as long as the switch is non-blocking (which all modern single-chassis switches are).
can you use multiple 100Mbit ports in full speed simultaneously to use the bandwith from the single Gbit port?
Yes. The higher-rate ports are intended for uplinking (=connecting to a larger infrastructure), ie. in a fat tree topology. But you can use them in any way you see fit.
E.g. you could connect your main server and a fast (Internet) router to 1G ports and put clients and smaller servers on the 100M ports. Or use a 1G port to link to another switch. Or ...
A switch generally buffers network frames, decoupling transmit and receive rates. That way, a server can transmit a frame at 1 Gbit/s and a client on another port can receive the exact same frame at 100 Mbit/s (or vice versa). Accordingly, a sufficiently fast server linked at 1 Gbit/s can simultaneously feed ten clients at 100 Mbit/s at their full rate.