A: Happily, nothing – unless you’re prone to allergies. Even then, not much. They’re not hurting the plants in your landscape.
There are several slime molds that pop up in decaying organic matter this time of year, such as the compost in your flower bed soil or decaying mulch. They’ll ooze up to the surface of the soil sometimes in the spring when the weather conditions are right. They’ll harden in place and eventually blow away on the wind, but they do not harm your plants unless they’re just covering the desirable plants such that the plants can’t get sunshine or rain. Picking these up with a flat-bottomed shovel and throwing them away is all we’d recommend.
The mushrooms are decaying the roots of the dead tree you removed for the next few years and are part of the natural cycle, again generally when we’ve had moisture and when soil temperatures are just right. Now, they’re not food (and could be dangerous to eat) – but these also are not hurting your healthy plants in the area. They won’t come up any more for the season once we get really hot, and once most of the roots have decayed they’ll stop altogether. Again, a shovel and a trash can is the answer.