Beginner knitter--color change questions

Hello! I am a reasonably new knitter with 2 questions really. The pattern that I am working calls for frequent color changes and slipping the first stitch of each row.

Question 1: do i slip the old color as the first stitch and then start the new color or how do I change so that it is the new color that I am slipping?

Question 2: Does anyone have a better technique than tying my two yarns together to join a new color? I tried the whole twisting the yarns together like my grandmother does but it was a nightmare. Now I am just tying a tiny knot close to the last stitch and then tucking both ends in.

Welcome to the forum!
What are you making? If this is a scarf, you could work the last stitch of the old color row with the new color. That’ll give you the new color as the slipped stitch on the next row at this end.
You can join with a loose knot and then go back later to undo the knot and weave in the ends. Cross the strands of both yarns so that you don’t see a hole when you look from the RS of the piece.

yes it is a scarf. A very long Dr Who scarf with 7 rotating colors. I will try that with the last stitch.