Electrical – Is it acceptable to splice a circuit in two opposite directions for outdoor recepts/lighting

You might want to look into using something like this...

Designed for paper lanterns.

Notice that the weight of the lights are supported by the cable and the socket, not the junction itself. The problem with the product you linked to, is the weight of the lights are supported by the junction (given that it's not mounted properly). Over time the weight (or accidental yanking) could cause the junction to separate, leading to a potential shock/fire hazard.

There's no problem with anything you've suggested. You can use a 15 ampere breaker to protect 14 AWG copper conductors, without a problem. If you feel that 15 amperes is not enough for the receptacles, there is no problem installing 12 AWG wire with a 20 ampere breaker. It's completely up to you what you think is best. If the cost difference is not prohibitive, it may be worth installing #12 on a 20A breaker. Especially if you think you might plug in multiple higher load items at the same time (George Foreman and electric mower for example), or may consider adding additional receptacles in the future.

There is also no problem using a junction box to provide power to different devices. As long as the box is properly installed, accessible, sized appropriately, and adequately sealed.

Nothing in electrical code says that lights and receptacles cannot be on the same circuit. It's more of a guideline than a rule. The general idea is that if the vacuum trips the breaker, you don't want to be left standing in the dark.

The only problem I see, is with the GFCI receptacles in your drawing. You will not need two GFCI receptacles. You'll simply feed the second receptacle, from the load side of the GFCI receptacle. When wired this way, the GFCI receptacle provides protection to the downstream receptacle.