I have only been following along, and as Tim has rightfully suggested, you have come a long way. You have also gotten a broad range of advice from contemporary metal fittings to make your table and now into more my world of "traditional joinery" so I thought it germane to add my two cents.
First I recall from earlier post that your wood may have a higher than normal moisture content for such work as a table for "regular" modern woodworking methods...As such, some more reading may help, if interested. The link below can take you to the list(s) I provide students.
Green Woodworking Booklist
I've seen these unglued as bedframes....
You may have...but it well may have been out of context, and/or other joinery at play that isn't understood. This type of joint does not have enough relish in the lap joint section to be secure for a table or a bead unless the cross sectional portions of the legs, runners and stretchers are huge...plus...other elements in the joinery as well. This is a common family of joints in Asian design modalities that I work in.
1. leave them unglued...4. glue and peg (ultimate security)...Would the glue prevent wood movement?
Yes, the glue would arrest movement too much and cause issues in a very short time...
3. peg (from the side into the tenons)
Yes, trunnel/peg could work and does in some forms of this joint but they don't go where you think they would...
Over all...this is a decorative joint, not very strong or functional at all. It is out of context for your intended application and there are severall much better traditional joints for such as you plan on building.