I believe it was explained that Jack Crusher, being integrated into the Borg, was still not fully under the control of the queen. When they saw the possible entry route Picard called it an opportunity. So I think Jack was helping them get in, maybe subconsciously.
Travel times in the Star Trek universe have always been inconsistent. They often seem to be able to get back to Earth in the blink of an eye, regardless of where they are in the galaxy. In Star Trek V, they're shown as travelling to the "center of the galaxy" in a matter of hours, when it should've taken decades, based on Star Trek's own theoretical warp speeds. It's all just a means to tell a story and keep dramatic pacing.
She said "trust no one," so she didn't want anyone else to be able to intercept her message. There's obviously a risk Picard doesn't hear his com badge, but there could be any number of in-world explanations for how com badges work and how it could alert the possesor of a message. Again, storytelling was the reason - they could've simply had the message come to him on a viewscreen as being encrypted, but they wanted to give the viewers a connection to who was sending it.