On the outdoor plants, basically no. You live in Minnesota which is not "tropical" so the native aquatic plants need a winter rest period and in a warm water tank would either die back for a period each year or perhaps die altogether. Aquarium plants are from the tropics and while some have periods of slow growth they generally (except for some Aponogeton species) do not hibernate or die back the way temperate plants must. Aside from this, there is the issue of pests and pathogens, but I won't get into that.
As for suitable plants for a 10g with a pair of dwarf cichlids, you can use the pygmy chain sword Echinodorus tenellus or any of the similar small chain swords. Echinodorus parviflorus 'Tropica' [Dwarf Sword] would be a nice contrast. You can find info on both these in our profiles section, second link from the left in the blue bar across the top, or click on the shaded name in posts to go to that profile.
Crypts would do well in this setup. Anubias is another slow growing plant that tolerates fairly heavy shade like crypts, and this is important in tanks with dwarf cichlids that do not appreciate light. Floating plants are necessary to calm the fish, and crypts and Anubias would do well under them. As would Java Fern and Java Moss.
For floating plants, Ceratopteris cornuta is ideal. The stem plant Brazilian Pennywort allowed to float is also good, I have this in a 10g window tank and the dwarf rasbora love it.
On planted tanks in general, there is a series of 4 articles at the head of this section entitled "A Basic Approach to the Natural Planted Aquarium" that should give you some background info. And questions are always welcome