The passage (1 Timothy 2:1-5) calls for intercession done by Timothy (for example) for the king (for example) to Christ, Who is the sole mediator to God the Father. The "sole mediator", therefore, does not prohibit mediation of Timothy to Christ, but if so, then also by Mary or any other saint to Christ.
No, Paul was writing a letter. It was written to a live person (Timothy) and to other live people who might read it. It was not written to any of the departed. Paul says "I urge, then, first of all, that requests, prayers, intercession and thanksgiving be made for everyone— for kings and all those in authority, ...". Paul is not urging the departed, he is urging live people, the audience for his letter. The assertion that this equally applies to the departed is completely fabricated by the Church. The Bible does not support it, in fact, the Bible leans against contacting the departed. Physical death is meant to be a separation. By faith, we will be reunited with our fellow Christian brothers and sisters in Christ one day. But that day isn't today. There is no logic at all to saying that since it is fine for me to ask you for prayer, it must be fine for me to pray to the departed. They are completely different things.