Oooh! Two big subjects John. I'm not sure how much experience with turning you have, but I'll give you my two penneth worth and I'm sure others will come by with some offerings too.
With regard to the box, generally you've got to find some way of reverse chucking the lid to finish its underside, so the generally accepted order of play is to make the outer side of the lid into a tenon fist, then part it off. There's a little trick about leaving a so called "witness mark" when you do so, but you've probably picked that up from youtube already. Make and finish the inside of the box section and as far as possible the outer side, then remove from chuck. Mount the lid using the tenon on outer side, make and finish the underside. Reverse chuck the lid using the underside as a chucking point, so think about how that's going to happen when you design your box, before you even mount any wood on the lathe. (Often it's possible to remount the box section and locate the lid in it, using the box section as a jam chuck with support from the tail stock, and often the underside features either a step of a recess which might conform to your chuck jaws, so you can mount it directly in the chuck, with a bit of tissue or something else to protect the finish). Make and finish the outer side of the lid. Reverse chuck the box section, make and finish underside. Remove from chuck. Put two halves together. Show partner. Price. Sell. Drink red wine. Sober up. Make another one.
With regard to the natural edge bowl, anything you remove on the bandsaw means less time and effort making shavings on the floor. I find it helpful to at least remove the corners on the bandsaw to make it an octagon. Cutting a log on a bandsaw can be a perilous task if you value your fingers, as it can rotate under the blade or kick back at you, so bear that in mind too and take great care. Youtube probably has lots or jigs on it for bandsawing logs.
And no, they're not daft questions. If you don't ask, you don't know. We all have to start somewhere.