Technically/theoretically yes, but in practice it is not really seen. The biggest reason is that spiders have huge strength compared to the size of their bodies and, therefore, can easily overpower the adhesive properties of their own webs. If they were to get stuck it would be by encasement since the web is, also, incredibly strong in tensile strength.
Yes, if it's not careful! Not all the lines are sticky, they memorize which is which! And if it does happen to step wrong, that leg is stuck but, they use the other 7 to free itself! If a different spider gets into the web, well, depends on the sex, type, and size!