I’m wanting to jump on the problem of these weeds being in my yard, what type of chemicals would I be able to apply to them and what are the types of weeds?
The first photo shows primarily violets, probably wood violets if you live in the northern US and east of the Mississippi River. In my experience, no chemical on earth will kill a violet, although I have heard that repeatedly spraying them with RoundUp over the course of several months may do the trick (part of the problem, I think, is that RoundUp is not taken up by the violet's stem, so it's able to resprout after a couple weeks).
Violets will outcompete fescues and ryegrass and will also hold their own against bluegrass. The only defense is hand-weeding. You may also want to know that they can set seed without any flower being pollinated, and that their seedpods "shatter" when ripe, scattering seed about a foot on all sides from the plant. This happens in late summer/early fall, so when you hand-pull makes a difference.
The second photo is more difficult to ID. It could be a strawberry of some kind (Fragraria genus) or more probably a potentilla (Potentilla indica, also known as cinquefoil or Indian Mock Strawberry). Strawberries have white flowers; potentillas yellow flowers. Any usual common broadleaf herbicide such as Weed-B-Gone would kill either plant.