The purple flowers are a variety of Crocus, a commonly-grown spring-flowering bulb. They are not considered weeds, though occasionally they can "naturalize" (spread without human involvement) by means of wildlife moving the bulbs around, or perhaps by seed. So far, they are not invasive in Maryland; one species of Crocus has naturalized a bit in wild areas, but it doesn't spread rampantly and should be easy to remove if you wanted to dig it out.

Crocus come in various shades of purple, yellow, and white. They flower in early spring and the foliage goes dormant by summer, so they will disappear from view within a couple months. Deer and squirrels (and possibly rabbits too) can enjoy eating the flowers, in case they suddenly disappear sooner.

The lower holly branches can be trimmed this month if you prefer to remove them (it won't hurt the tree any to keep them). No, do not apply anything to the wound, as that can interfere with them sealing-over. You can use the guidance on how to make proper pruning cuts in the linked page, since you should not make the cut too close to the trunk to avoid the risk of introducing wood decay. If you find the pruning daunting, you could hire a certified arborist or licensed tree expert to do the pruning for you (make sure they have either of these certifications so they are well-trained).

Miri