My house's basement has wood shelves that are firmly attached to the basement's concrete walls. I need to remove these shelves (because of molding issues) but my drill is not strong enough to detach the screws. Can anyone recommend a suitable type of drill for this job. Thank you so much.
For the first one, an appropriate sized 6-point socket, and a ratchet (wrench)
For the second one, the correct size of Phillips bit (likely a #3) and a socket to fit that bit, and a ratchet.
i.e. not a drill at all.
Depending on age and corrosion, the screws may break rather than turning. In that case, remove the remains with a cutting disk in a grinder, doing so at a time when you will be present and awake for hours afterwards, lest a spark from cutting should lurk somewhere and start a fire.
The color and application suggest that these are Tap-Con® screws directly into concrete.