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Purslane actually comes in a variety of colors, which can range from white, pink and rose to shades of yellow and orange. There are even lavender varieties as well as multi-colored types. Typically, wild purslane (which is commonly considered a weed) has yellow blooms while the other types of purslane are nursery grown types that are available in numerous colors.

Are you covering the seeds? Portulaca seeds need light to germinate and should not be covered.

Purselane seeds on the other hand, needs to be chilled for a few weeks in order to germinate.

These articles may help: https://www.gardeningknowhow.com/edible/herbs/purslane/edible-purslane-herb.htm
https://www.gardeningknowhow.com/ornamental/flowers/portulaca/portulaca-plants.htm

As soon as the temps outside warm up and remain a consistent 50-60 degrees or more, preferably at night, and the threat of frost/freezing temps. has ceased. The plant needs to be properly acclimated first. It may exhibit some leaf yellowing and dropping while adapting to the new surrounding but this should cease on its own. Here is an article or two that you may find helpful: https://www.gardeningknowhow.com/houseplants/hpgen/move-houseplant-outside.htm, https://www.gardeningknowhow.com/houseplants/hpgen/acclimating-houseplants-outdoors.htm

This article will help with that: https://www.gardeningknowhow.com/plant-problems/weeds/purslane-control.htm

You can eat both. Lamb's lettuce will have a feel similar to bibb lettuce. Purslane is a succulent and so will feel fleshy, like a cactus or sedum.