solanum
The Solanum genus contains the eggplant, tomato and potato along with others such as woody nightshade.
Ranunculus
primula
I am not sure what you mean by classification. If you mean this in a culinary sense, I imagine it would be classified as a starch. Botanically speaking, the yam is a member of the Dioscorea genus. It should not be confused with the sweet potato (Ipomoea genus) or the common potato (Solanum genus). All of these plants are in different plant families.
A blazingstar is any of a group of plants of the genus Liatris, native to North America, including Mexico.
An althea is any of a group of plants belonging to the genus Althaea, including the hollyhocks and mallows, which are native to Eurasia.
Any of various plants of the genus Brassica of the mustard family, including cabbage, broccoli, and turnip. Source: Answers.com
The eggplant, aubergine, melongene, brinjal, or guinea squash (Solanum melongena) is a plant of the family Solanaceae (also known as the nightshades) and genus Solanum. It bears a fruit of the same name, commonly used as a vegetable in cooking. As a nightshade, it is closely related to thetomato and potato and is native to Nepal, India, Bangladesh, Pakistan, and Sri Lanka.
Those tomato-like objects are the potato fruit, containing seeds. Tomato and Potato are closely related, in the same genus, and the fruit are therefore very similar in structure. There is however one important difference - Potato fruit are poisonous, so don't eat them. When they are fully ripe, you could harvest the seed from them to sow next spring, though the quality of the potatoes produced by plants grown from the seed might not be too good.
Arrowhead
plants does not have any particular genus
Genus and species are specific to each individual organism, so there is no genus species for all plants.